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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3,901 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 0.8923 m | An object of mass 7.905 kg is released from rest at height 0.8923 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) = 4.183 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. |
3,902 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 24.09 m | An object of mass 15.7 kg is released from rest at height 24.09 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) = 21.74 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. |
3,903 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 26.88 m | An object of mass 1.741 kg is released from rest at height 26.88 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) = 22.96 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. |
3,904 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 13.29 m | An object of mass 12.41 kg is released from rest at height 13.29 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) = 16.14 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. |
3,905 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 37.59 m | An object of mass 19.73 kg is released from rest at height 37.59 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) = 27.15 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. |
3,906 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 29.6 m | An object of mass 14.91 kg is released from rest at height 29.6 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) = 24.09 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. |
3,907 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 6.445 m | An object of mass 6.467 kg is released from rest at height 6.445 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) = 11.24 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. |
3,908 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 6.326 m | An object of mass 9.281 kg is released from rest at height 6.326 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) = 11.14 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. |
3,909 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 4.987 m | An object of mass 17.31 kg is released from rest at height 4.987 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) = 9.89 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. |
3,910 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 16.55 m | An object of mass 19.41 kg is released from rest at height 16.55 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) = 18.02 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. |
3,911 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 0.6452 m | An object of mass 10.51 kg is released from rest at height 0.6452 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) = 3.557 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. |
3,912 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 33.38 m | An object of mass 9.121 kg is released from rest at height 33.38 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) = 25.59 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. |
3,913 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 18.25 m | An object of mass 2.689 kg is released from rest at height 18.25 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) = 18.92 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. |
3,914 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 4.349 m | An object of mass 19.4 kg is released from rest at height 4.349 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) = 9.236 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. |
3,915 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 39.17 m | An object of mass 4.529 kg is released from rest at height 39.17 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) = 27.72 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. |
3,916 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 22.07 m | An object of mass 8.519 kg is released from rest at height 22.07 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) = 20.81 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. |
3,917 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 15.41 m | An object of mass 3.489 kg is released from rest at height 15.41 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) = 17.39 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. |
3,918 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 38.12 m | An object of mass 7.092 kg is released from rest at height 38.12 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) = 27.34 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. |
3,919 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 23.29 m | An object of mass 19.44 kg is released from rest at height 23.29 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) = 21.37 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. |
3,920 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 32.64 m | An object of mass 0.4845 kg is released from rest at height 32.64 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) = 25.3 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. |
3,921 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 35.92 m | An object of mass 0.5206 kg is released from rest at height 35.92 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) = 26.54 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. |
3,922 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 34.78 m | An object of mass 10.14 kg is released from rest at height 34.78 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) = 26.12 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. |
3,923 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 26.13 m | An object of mass 14.05 kg is released from rest at height 26.13 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) = 22.64 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. |
3,924 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 16.71 m | An object of mass 9.229 kg is released from rest at height 16.71 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) = 18.1 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. |
3,925 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 21.93 m | An object of mass 7.174 kg is released from rest at height 21.93 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) = 20.74 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. |
3,926 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 30.72 m | An object of mass 10.56 kg is released from rest at height 30.72 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) = 24.55 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. |
3,927 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 7.445 m | An object of mass 2.445 kg is released from rest at height 7.445 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) = 12.08 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. |
3,928 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 7.487 m | An object of mass 8.682 kg is released from rest at height 7.487 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) = 12.12 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. |
3,929 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 21.94 m | An object of mass 11.98 kg is released from rest at height 21.94 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) = 20.74 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. |
3,930 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 33.88 m | An object of mass 7.755 kg is released from rest at height 33.88 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) = 25.78 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. |
3,931 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 17.78 m | An object of mass 13.83 kg is released from rest at height 17.78 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) = 18.67 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. |
3,932 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 25 m | An object of mass 5.808 kg is released from rest at height 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) = 22.15 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. |
3,933 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 34.35 m | An object of mass 18.52 kg is released from rest at height 34.35 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) = 25.96 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. |
3,934 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 32.33 m | An object of mass 19.91 kg is released from rest at height 32.33 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) = 25.18 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. |
3,935 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 26.16 m | An object of mass 2.255 kg is released from rest at height 26.16 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) = 22.65 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. |
3,936 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 16.75 m | An object of mass 12.4 kg is released from rest at height 16.75 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) = 18.12 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. |
3,937 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 30.19 m | An object of mass 10.03 kg is released from rest at height 30.19 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) = 24.33 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. |
3,938 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 4.438 m | An object of mass 18.56 kg is released from rest at height 4.438 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) = 9.33 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. |
3,939 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 23.46 m | An object of mass 8.993 kg is released from rest at height 23.46 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) = 21.45 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. |
3,940 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 11.95 m | An object of mass 0.8462 kg is released from rest at height 11.95 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) = 15.31 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. |
3,941 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 9.304 m | An object of mass 8.529 kg is released from rest at height 9.304 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) = 13.51 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. |
3,942 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 15.55 m | An object of mass 9.202 kg is released from rest at height 15.55 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) = 17.47 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. |
3,943 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 19.05 m | An object of mass 4.072 kg is released from rest at height 19.05 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) = 19.33 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. |
3,944 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 38.72 m | An object of mass 2.664 kg is released from rest at height 38.72 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) = 27.56 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. |
3,945 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 16.81 m | An object of mass 18.3 kg is released from rest at height 16.81 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) = 18.16 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. |
3,946 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 28.3 m | An object of mass 16.44 kg is released from rest at height 28.3 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) = 23.56 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. |
3,947 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 0.8004 m | An object of mass 14.87 kg is released from rest at height 0.8004 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) = 3.962 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. |
3,948 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 9.345 m | An object of mass 7.618 kg is released from rest at height 9.345 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) = 13.54 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. |
3,949 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 35.24 m | An object of mass 5.815 kg is released from rest at height 35.24 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) = 26.29 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. |
3,950 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 13.3 m, speed 33.7 m/s | An object moves in a circle of radius 13.3 m at constant speed 33.7 m/s. The centripetal acceleration has magnitude a_c = v² / r = 85.4 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. |
3,951 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 39.78 m, speed 17.17 m/s | An object moves in a circle of radius 39.78 m at constant speed 17.17 m/s. The centripetal acceleration has magnitude a_c = v² / r = 7.415 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. |
3,952 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 12.15 m, speed 36.11 m/s | An object moves in a circle of radius 12.15 m at constant speed 36.11 m/s. The centripetal acceleration has magnitude a_c = v² / r = 107.3 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. |
3,953 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 20.79 m, speed 1.606 m/s | An object moves in a circle of radius 20.79 m at constant speed 1.606 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.124 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. |
3,954 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 7.753 m, speed 15.6 m/s | An object moves in a circle of radius 7.753 m at constant speed 15.6 m/s. The centripetal acceleration has magnitude a_c = v² / r = 31.39 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. |
3,955 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 40.85 m, speed 32.98 m/s | An object moves in a circle of radius 40.85 m at constant speed 32.98 m/s. The centripetal acceleration has magnitude a_c = v² / r = 26.63 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. |
3,956 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 30.04 m, speed 14.07 m/s | An object moves in a circle of radius 30.04 m at constant speed 14.07 m/s. The centripetal acceleration has magnitude a_c = v² / r = 6.589 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. |
3,957 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 47.96 m, speed 39.72 m/s | An object moves in a circle of radius 47.96 m at constant speed 39.72 m/s. The centripetal acceleration has magnitude a_c = v² / r = 32.89 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. |
3,958 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 12.17 m, speed 38.97 m/s | An object moves in a circle of radius 12.17 m at constant speed 38.97 m/s. The centripetal acceleration has magnitude a_c = v² / r = 124.8 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. |
3,959 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 9.714 m, speed 26.13 m/s | An object moves in a circle of radius 9.714 m at constant speed 26.13 m/s. The centripetal acceleration has magnitude a_c = v² / r = 70.31 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. |
3,960 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 41.44 m, speed 32.25 m/s | An object moves in a circle of radius 41.44 m at constant speed 32.25 m/s. The centripetal acceleration has magnitude a_c = v² / r = 25.1 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. |
3,961 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 28.93 m, speed 6.026 m/s | An object moves in a circle of radius 28.93 m at constant speed 6.026 m/s. The centripetal acceleration has magnitude a_c = v² / r = 1.255 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. |
3,962 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 31.85 m, speed 39.12 m/s | An object moves in a circle of radius 31.85 m at constant speed 39.12 m/s. The centripetal acceleration has magnitude a_c = v² / r = 48.04 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. |
3,963 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 8.768 m, speed 36.26 m/s | An object moves in a circle of radius 8.768 m at constant speed 36.26 m/s. The centripetal acceleration has magnitude a_c = v² / r = 150 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. |
3,964 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 25.91 m, speed 18.06 m/s | An object moves in a circle of radius 25.91 m at constant speed 18.06 m/s. The centripetal acceleration has magnitude a_c = v² / r = 12.59 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. |
3,965 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 5.069 m, speed 32.25 m/s | An object moves in a circle of radius 5.069 m at constant speed 32.25 m/s. The centripetal acceleration has magnitude a_c = v² / r = 205.1 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. |
3,966 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 25.26 m, speed 25.63 m/s | An object moves in a circle of radius 25.26 m at constant speed 25.63 m/s. The centripetal acceleration has magnitude a_c = v² / r = 26 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. |
3,967 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 39.24 m, speed 33.88 m/s | An object moves in a circle of radius 39.24 m at constant speed 33.88 m/s. The centripetal acceleration has magnitude a_c = v² / r = 29.25 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. |
3,968 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 31.4 m, speed 11.15 m/s | An object moves in a circle of radius 31.4 m at constant speed 11.15 m/s. The centripetal acceleration has magnitude a_c = v² / r = 3.958 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. |
3,969 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 27.69 m, speed 38 m/s | An object moves in a circle of radius 27.69 m at constant speed 38 m/s. The centripetal acceleration has magnitude a_c = v² / r = 52.15 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. |
3,970 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 10.27 m, speed 4.637 m/s | An object moves in a circle of radius 10.27 m at constant speed 4.637 m/s. The centripetal acceleration has magnitude a_c = v² / r = 2.094 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. |
3,971 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 21.93 m, speed 25.53 m/s | An object moves in a circle of radius 21.93 m at constant speed 25.53 m/s. The centripetal acceleration has magnitude a_c = v² / r = 29.72 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. |
3,972 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 29.71 m, speed 2.085 m/s | An object moves in a circle of radius 29.71 m at constant speed 2.085 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.1463 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. |
3,973 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 35.41 m, speed 36.9 m/s | An object moves in a circle of radius 35.41 m at constant speed 36.9 m/s. The centripetal acceleration has magnitude a_c = v² / r = 38.46 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. |
3,974 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 4.031 m, speed 15.91 m/s | An object moves in a circle of radius 4.031 m at constant speed 15.91 m/s. The centripetal acceleration has magnitude a_c = v² / r = 62.83 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. |
3,975 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 37.14 m, speed 6.091 m/s | An object moves in a circle of radius 37.14 m at constant speed 6.091 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.999 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. |
3,976 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 22.74 m, speed 25.63 m/s | An object moves in a circle of radius 22.74 m at constant speed 25.63 m/s. The centripetal acceleration has magnitude a_c = v² / r = 28.88 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. |
3,977 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 17.97 m, speed 10.35 m/s | An object moves in a circle of radius 17.97 m at constant speed 10.35 m/s. The centripetal acceleration has magnitude a_c = v² / r = 5.96 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. |
3,978 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 44.91 m, speed 12.58 m/s | An object moves in a circle of radius 44.91 m at constant speed 12.58 m/s. The centripetal acceleration has magnitude a_c = v² / r = 3.524 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. |
3,979 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 26.82 m, speed 10.56 m/s | An object moves in a circle of radius 26.82 m at constant speed 10.56 m/s. The centripetal acceleration has magnitude a_c = v² / r = 4.162 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. |
3,980 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 39.02 m, speed 31.66 m/s | An object moves in a circle of radius 39.02 m at constant speed 31.66 m/s. The centripetal acceleration has magnitude a_c = v² / r = 25.68 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. |
3,981 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 38.54 m, speed 26.71 m/s | An object moves in a circle of radius 38.54 m at constant speed 26.71 m/s. The centripetal acceleration has magnitude a_c = v² / r = 18.51 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. |
3,982 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 13.82 m, speed 37.46 m/s | An object moves in a circle of radius 13.82 m at constant speed 37.46 m/s. The centripetal acceleration has magnitude a_c = v² / r = 101.6 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. |
3,983 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 31.41 m, speed 25.9 m/s | An object moves in a circle of radius 31.41 m at constant speed 25.9 m/s. The centripetal acceleration has magnitude a_c = v² / r = 21.35 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. |
3,984 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 29.01 m, speed 5.033 m/s | An object moves in a circle of radius 29.01 m at constant speed 5.033 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.8733 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. |
3,985 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 23.01 m, speed 24.24 m/s | An object moves in a circle of radius 23.01 m at constant speed 24.24 m/s. The centripetal acceleration has magnitude a_c = v² / r = 25.53 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. |
3,986 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 5.443 m, speed 12.02 m/s | An object moves in a circle of radius 5.443 m at constant speed 12.02 m/s. The centripetal acceleration has magnitude a_c = v² / r = 26.53 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. |
3,987 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 44.74 m, speed 4.618 m/s | An object moves in a circle of radius 44.74 m at constant speed 4.618 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.4767 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. |
3,988 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 24.76 m, speed 15.09 m/s | An object moves in a circle of radius 24.76 m at constant speed 15.09 m/s. The centripetal acceleration has magnitude a_c = v² / r = 9.201 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. |
3,989 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 41.93 m, speed 16.24 m/s | An object moves in a circle of radius 41.93 m at constant speed 16.24 m/s. The centripetal acceleration has magnitude a_c = v² / r = 6.291 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. |
3,990 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 24.6 m, speed 1.856 m/s | An object moves in a circle of radius 24.6 m at constant speed 1.856 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.1401 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. |
3,991 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 3.771 m, speed 38.41 m/s | An object moves in a circle of radius 3.771 m at constant speed 38.41 m/s. The centripetal acceleration has magnitude a_c = v² / r = 391.2 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. |
3,992 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 3.908 m, speed 27.81 m/s | An object moves in a circle of radius 3.908 m at constant speed 27.81 m/s. The centripetal acceleration has magnitude a_c = v² / r = 197.8 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. |
3,993 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 18.83 m, speed 13.23 m/s | An object moves in a circle of radius 18.83 m at constant speed 13.23 m/s. The centripetal acceleration has magnitude a_c = v² / r = 9.298 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. |
3,994 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 45.42 m, speed 32.53 m/s | An object moves in a circle of radius 45.42 m at constant speed 32.53 m/s. The centripetal acceleration has magnitude a_c = v² / r = 23.3 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. |
3,995 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 9.072 m, speed 1.395 m/s | An object moves in a circle of radius 9.072 m at constant speed 1.395 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.2146 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. |
3,996 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 9.016 m, speed 23.12 m/s | An object moves in a circle of radius 9.016 m at constant speed 23.12 m/s. The centripetal acceleration has magnitude a_c = v² / r = 59.31 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. |
3,997 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 30.37 m, speed 2.227 m/s | An object moves in a circle of radius 30.37 m at constant speed 2.227 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.1632 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. |
3,998 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 48.8 m, speed 39.76 m/s | An object moves in a circle of radius 48.8 m at constant speed 39.76 m/s. The centripetal acceleration has magnitude a_c = v² / r = 32.39 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. |
3,999 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 24.25 m, speed 24.95 m/s | An object moves in a circle of radius 24.25 m at constant speed 24.95 m/s. The centripetal acceleration has magnitude a_c = v² / r = 25.67 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. |
4,000 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 27.37 m, speed 7.177 m/s | An object moves in a circle of radius 27.37 m at constant speed 7.177 m/s. The centripetal acceleration has magnitude a_c = v² / r = 1.882 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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