id int64 1 14M | domain stringclasses 6
values | topic stringclasses 23
values | subtopic stringclasses 37
values | difficulty int64 1 8 | unit_type stringclasses 3
values | title stringlengths 14 86 | content stringlengths 203 553 | key_equations stringclasses 23
values | prerequisites stringclasses 29
values | learning_objective stringclasses 37
values |
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5,601 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 1.024 m | An object of mass 3.665 kg is released from rest at height 1.024 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 4.482 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,602 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 26.44 m | An object of mass 17.97 kg is released from rest at height 26.44 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 22.77 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,603 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 35.12 m | An object of mass 19.2 kg is released from rest at height 35.12 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 26.24 m/s at the reference leve... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,604 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 28.9 m | An object of mass 14.26 kg is released from rest at height 28.9 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 23.81 m/s at the reference leve... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,605 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 11.06 m | An object of mass 4.213 kg is released from rest at height 11.06 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 14.73 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,606 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 38.55 m | An object of mass 13.49 kg is released from rest at height 38.55 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 27.5 m/s at the reference leve... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,607 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 27.74 m | An object of mass 3.924 kg is released from rest at height 27.74 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 23.33 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,608 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 39.84 m | An object of mass 16.25 kg is released from rest at height 39.84 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 27.95 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,609 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 22.75 m | An object of mass 1.074 kg is released from rest at height 22.75 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 21.12 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,610 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 22.58 m | An object of mass 17.17 kg is released from rest at height 22.58 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 21.04 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,611 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 31.78 m | An object of mass 14.12 kg is released from rest at height 31.78 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 24.97 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,612 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 29.83 m | An object of mass 14.37 kg is released from rest at height 29.83 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 24.19 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,613 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 3.992 m | An object of mass 5.873 kg is released from rest at height 3.992 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 8.849 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,614 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 32.92 m | An object of mass 7.472 kg is released from rest at height 32.92 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 25.41 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,615 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 15.24 m | An object of mass 10.98 kg is released from rest at height 15.24 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 17.29 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,616 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 29.18 m | An object of mass 18.06 kg is released from rest at height 29.18 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 23.93 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,617 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 13.17 m | An object of mass 10.91 kg is released from rest at height 13.17 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 16.07 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,618 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 16.58 m | An object of mass 12.86 kg is released from rest at height 16.58 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 18.03 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,619 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 15.2 m | An object of mass 11.69 kg is released from rest at height 15.2 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 17.27 m/s at the reference leve... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,620 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 30.81 m | An object of mass 19.67 kg is released from rest at height 30.81 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 24.58 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,621 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 27.07 m | An object of mass 3.123 kg is released from rest at height 27.07 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 23.04 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,622 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 27.19 m | An object of mass 17.81 kg is released from rest at height 27.19 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 23.09 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,623 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 38.47 m | An object of mass 8.275 kg is released from rest at height 38.47 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 27.47 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,624 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 10.5 m | An object of mass 1.912 kg is released from rest at height 10.5 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 14.35 m/s at the reference leve... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,625 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 37.03 m | An object of mass 2.925 kg is released from rest at height 37.03 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 26.95 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,626 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 18.31 m | An object of mass 12.98 kg is released from rest at height 18.31 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 18.95 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,627 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 27.37 m | An object of mass 10.88 kg is released from rest at height 27.37 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 23.17 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,628 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 14.07 m | An object of mass 17.82 kg is released from rest at height 14.07 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 16.61 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,629 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 39.32 m | An object of mass 18.38 kg is released from rest at height 39.32 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 27.77 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,630 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 14 m | An object of mass 3.072 kg is released from rest at height 14 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 16.57 m/s at the reference level.... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,631 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 29.92 m | An object of mass 12.73 kg is released from rest at height 29.92 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 24.22 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,632 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 23.16 m | An object of mass 17.05 kg is released from rest at height 23.16 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 21.31 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,633 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 31.79 m | An object of mass 19.55 kg is released from rest at height 31.79 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 24.97 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,634 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 16.16 m | An object of mass 16.53 kg is released from rest at height 16.16 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 17.8 m/s at the reference leve... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,635 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 35.29 m | An object of mass 16.5 kg is released from rest at height 35.29 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 26.31 m/s at the reference leve... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,636 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 21.99 m | An object of mass 19.81 kg is released from rest at height 21.99 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 20.77 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,637 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 23.23 m | An object of mass 10.49 kg is released from rest at height 23.23 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 21.35 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,638 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 22.24 m | An object of mass 5.243 kg is released from rest at height 22.24 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 20.89 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,639 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 29.72 m | An object of mass 18.86 kg is released from rest at height 29.72 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 24.14 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,640 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 31.62 m | An object of mass 13.74 kg is released from rest at height 31.62 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 24.9 m/s at the reference leve... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,641 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 13.36 m | An object of mass 9.886 kg is released from rest at height 13.36 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 16.19 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,642 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 15.25 m | An object of mass 16.76 kg is released from rest at height 15.25 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 17.29 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,643 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 21.16 m | An object of mass 18.75 kg is released from rest at height 21.16 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 20.37 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,644 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 9.153 m | An object of mass 16.42 kg is released from rest at height 9.153 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 13.4 m/s at the reference leve... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,645 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 16.62 m | An object of mass 7.152 kg is released from rest at height 16.62 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 18.05 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,646 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 4.704 m | An object of mass 15.08 kg is released from rest at height 4.704 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 9.605 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,647 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 18.42 m | An object of mass 12.88 kg is released from rest at height 18.42 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 19.01 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,648 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 35.86 m | An object of mass 16.72 kg is released from rest at height 35.86 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 26.52 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,649 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 0.5235 m | An object of mass 3.929 kg is released from rest at height 0.5235 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 3.204 m/s at the reference le... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,650 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 20.43 m | An object of mass 15.91 kg is released from rest at height 20.43 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 20.02 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,651 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 6.202 m | An object of mass 2.334 kg is released from rest at height 6.202 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 11.03 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,652 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 38.03 m | An object of mass 1.63 kg is released from rest at height 38.03 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 27.31 m/s at the reference leve... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,653 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 16.54 m | An object of mass 4.988 kg is released from rest at height 16.54 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 18.01 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,654 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 21.91 m | An object of mass 16.54 kg is released from rest at height 21.91 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 20.73 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,655 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 32.67 m | An object of mass 2.112 kg is released from rest at height 32.67 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 25.31 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,656 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 1.728 m | An object of mass 0.6654 kg is released from rest at height 1.728 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 5.822 m/s at the reference le... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,657 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 7.836 m | An object of mass 2.597 kg is released from rest at height 7.836 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 12.4 m/s at the reference leve... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,658 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 3.318 m | An object of mass 15.57 kg is released from rest at height 3.318 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 8.067 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,659 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 38.06 m | An object of mass 5.218 kg is released from rest at height 38.06 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 27.32 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,660 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 14.62 m | An object of mass 8.554 kg is released from rest at height 14.62 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 16.93 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,661 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 28.06 m | An object of mass 8.179 kg is released from rest at height 28.06 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 23.46 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,662 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 15.82 m | An object of mass 6.144 kg is released from rest at height 15.82 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 17.61 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,663 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 17.43 m | An object of mass 4.327 kg is released from rest at height 17.43 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 18.49 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,664 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 19.4 m | An object of mass 11.88 kg is released from rest at height 19.4 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 19.51 m/s at the reference leve... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,665 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 2.154 m | An object of mass 12.37 kg is released from rest at height 2.154 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 6.5 m/s at the reference level... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,666 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 1.745 m | An object of mass 9.928 kg is released from rest at height 1.745 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 5.85 m/s at the reference leve... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,667 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 1.726 m | An object of mass 6.529 kg is released from rest at height 1.726 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 5.818 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,668 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 34.52 m | An object of mass 14.07 kg is released from rest at height 34.52 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 26.02 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,669 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 21.79 m | An object of mass 7.798 kg is released from rest at height 21.79 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 20.67 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,670 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 27.7 m | An object of mass 2.141 kg is released from rest at height 27.7 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 23.31 m/s at the reference leve... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,671 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 14.37 m | An object of mass 12.48 kg is released from rest at height 14.37 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 16.79 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,672 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 19.87 m | An object of mass 19.43 kg is released from rest at height 19.87 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 19.74 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,673 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 2.028 m | An object of mass 0.7411 kg is released from rest at height 2.028 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 6.306 m/s at the reference le... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,674 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 36.28 m | An object of mass 9.851 kg is released from rest at height 36.28 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 26.68 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,675 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 21.98 m | An object of mass 9.602 kg is released from rest at height 21.98 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 20.76 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,676 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 29.11 m | An object of mass 1.843 kg is released from rest at height 29.11 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 23.89 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,677 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 36.93 m | An object of mass 14.37 kg is released from rest at height 36.93 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 26.91 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,678 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 30.09 m | An object of mass 9.203 kg is released from rest at height 30.09 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 24.29 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,679 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 39.37 m | An object of mass 4.979 kg is released from rest at height 39.37 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 27.79 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,680 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 12.74 m | An object of mass 0.88 kg is released from rest at height 12.74 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 15.81 m/s at the reference leve... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,681 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 34.26 m | An object of mass 15.59 kg is released from rest at height 34.26 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 25.92 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,682 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 16.72 m | An object of mass 4.488 kg is released from rest at height 16.72 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 18.11 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,683 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 5.571 m | An object of mass 0.4038 kg is released from rest at height 5.571 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 10.45 m/s at the reference le... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,684 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 31.34 m | An object of mass 17.28 kg is released from rest at height 31.34 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 24.79 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,685 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 18.05 m | An object of mass 18.72 kg is released from rest at height 18.05 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 18.82 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,686 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 18.8 m | An object of mass 10.14 kg is released from rest at height 18.8 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 19.2 m/s at the reference level... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
5,687 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 34.89 m, speed 16.14 m/s | An object moves in a circle of radius 34.89 m at constant speed 16.14 m/s. The centripetal acceleration has magnitude a_c = v² / r = 7.466 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,688 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 46.26 m, speed 26.49 m/s | An object moves in a circle of radius 46.26 m at constant speed 26.49 m/s. The centripetal acceleration has magnitude a_c = v² / r = 15.18 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,689 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 2.531 m, speed 23.84 m/s | An object moves in a circle of radius 2.531 m at constant speed 23.84 m/s. The centripetal acceleration has magnitude a_c = v² / r = 224.6 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,690 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 34.94 m, speed 20.15 m/s | An object moves in a circle of radius 34.94 m at constant speed 20.15 m/s. The centripetal acceleration has magnitude a_c = v² / r = 11.62 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,691 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 45.12 m, speed 12.44 m/s | An object moves in a circle of radius 45.12 m at constant speed 12.44 m/s. The centripetal acceleration has magnitude a_c = v² / r = 3.431 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,692 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 8.221 m, speed 12.32 m/s | An object moves in a circle of radius 8.221 m at constant speed 12.32 m/s. The centripetal acceleration has magnitude a_c = v² / r = 18.47 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,693 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 16.64 m, speed 5.277 m/s | An object moves in a circle of radius 16.64 m at constant speed 5.277 m/s. The centripetal acceleration has magnitude a_c = v² / r = 1.674 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,694 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 7.824 m, speed 33.66 m/s | An object moves in a circle of radius 7.824 m at constant speed 33.66 m/s. The centripetal acceleration has magnitude a_c = v² / r = 144.8 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,695 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 10.04 m, speed 19.96 m/s | An object moves in a circle of radius 10.04 m at constant speed 19.96 m/s. The centripetal acceleration has magnitude a_c = v² / r = 39.71 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,696 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 0.3841 m, speed 31.25 m/s | An object moves in a circle of radius 0.3841 m at constant speed 31.25 m/s. The centripetal acceleration has magnitude a_c = v² / r = 2543 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,697 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 40.36 m, speed 36.31 m/s | An object moves in a circle of radius 40.36 m at constant speed 36.31 m/s. The centripetal acceleration has magnitude a_c = v² / r = 32.67 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,698 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 38.65 m, speed 2.711 m/s | An object moves in a circle of radius 38.65 m at constant speed 2.711 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.1902 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,699 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 9.216 m, speed 14.26 m/s | An object moves in a circle of radius 9.216 m at constant speed 14.26 m/s. The centripetal acceleration has magnitude a_c = v² / r = 22.07 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,700 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 34.18 m, speed 33.98 m/s | An object moves in a circle of radius 34.18 m at constant speed 33.98 m/s. The centripetal acceleration has magnitude a_c = v² / r = 33.77 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
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