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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401 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 4.411 m | An object of mass 8.415 kg is released from rest at height 4.411 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) = 9.302 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. |
402 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 16.62 m | An object of mass 9.889 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) = 18.06 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. |
403 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 1.792 m | An object of mass 19.04 kg is released from rest at height 1.792 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) = 5.929 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. |
404 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 18.01 m | An object of mass 7.536 kg is released from rest at height 18.01 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) = 18.8 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. |
405 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 34.29 m | An object of mass 19.02 kg is released from rest at height 34.29 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) = 25.93 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. |
406 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 27.58 m | An object of mass 2.167 kg is released from rest at height 27.58 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) = 23.26 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. |
407 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 39.12 m | An object of mass 10.98 kg is released from rest at height 39.12 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) = 27.7 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. |
408 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 16.23 m | An object of mass 7.302 kg is released from rest at height 16.23 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) = 17.84 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. |
409 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 5.325 m | An object of mass 3.958 kg is released from rest at height 5.325 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) = 10.22 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. |
410 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 18.46 m | An object of mass 16.99 kg is released from rest at height 18.46 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) = 19.03 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. |
411 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 25.85 m | An object of mass 13.32 kg is released from rest at height 25.85 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) = 22.52 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. |
412 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 1.344 m | An object of mass 12.02 kg is released from rest at height 1.344 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) = 5.133 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. |
413 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 10.12 m | An object of mass 15.78 kg is released from rest at height 10.12 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) = 14.09 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. |
414 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 22.8 m | An object of mass 2.693 kg is released from rest at height 22.8 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) = 21.15 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. |
415 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 30.72 m | An object of mass 1.558 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. |
416 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 9.03 m | An object of mass 4.302 kg is released from rest at height 9.03 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) = 13.31 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. |
417 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 13.48 m | An object of mass 17.42 kg is released from rest at height 13.48 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) = 16.26 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. |
418 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 36.07 m | An object of mass 3.122 kg is released from rest at height 36.07 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) = 26.6 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. |
419 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 34.41 m | An object of mass 0.2561 kg is released from rest at height 34.41 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) = 25.98 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. |
420 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 5.635 m | An object of mass 3.065 kg is released from rest at height 5.635 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) = 10.51 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. |
421 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 7.393 m | An object of mass 5.163 kg is released from rest at height 7.393 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) = 12.04 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. |
422 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 1.518 m | An object of mass 13.29 kg is released from rest at height 1.518 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) = 5.457 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. |
423 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 31.7 m | An object of mass 0.4942 kg is released from rest at height 31.7 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) = 24.94 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. |
424 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 13.29 m | An object of mass 4.911 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. |
425 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 2.57 m | An object of mass 3.65 kg is released from rest at height 2.57 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) = 7.099 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. |
426 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 21.28 m | An object of mass 14.89 kg is released from rest at height 21.28 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) = 20.43 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. |
427 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 19.31 m | An object of mass 14.96 kg is released from rest at height 19.31 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) = 19.46 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. |
428 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 20.77 m | An object of mass 15.6 kg is released from rest at height 20.77 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) = 20.18 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. |
429 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 20.4 m | An object of mass 2.359 kg is released from rest at height 20.4 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) = 20 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. |
430 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 2.213 m | An object of mass 18.92 kg is released from rest at height 2.213 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) = 6.588 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. |
431 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 34.75 m | An object of mass 15.71 kg is released from rest at height 34.75 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) = 26.11 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. |
432 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 18.59 m | An object of mass 10.52 kg is released from rest at height 18.59 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) = 19.1 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. |
433 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 2.903 m | An object of mass 19.29 kg is released from rest at height 2.903 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) = 7.545 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. |
434 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 16.36 m | An object of mass 9.684 kg is released from rest at height 16.36 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) = 17.92 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. |
435 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 19.87 m | An object of mass 13.78 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. |
436 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 3.403 m | An object of mass 18.21 kg is released from rest at height 3.403 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) = 8.17 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. |
437 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 24.53 m | An object of mass 1.8 kg is released from rest at height 24.53 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) = 21.93 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. |
438 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 11.36 m | An object of mass 1.501 kg is released from rest at height 11.36 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) = 14.93 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. |
439 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 22.16 m | An object of mass 12.73 kg is released from rest at height 22.16 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) = 20.85 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. |
440 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 39.79 m | An object of mass 6.639 kg is released from rest at height 39.79 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) = 27.94 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. |
441 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 18.42 m | An object of mass 10.71 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. |
442 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 4.418 m | An object of mass 12.19 kg is released from rest at height 4.418 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) = 9.308 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. |
443 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 34.19 m | An object of mass 14.1 kg is released from rest at height 34.19 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) = 25.89 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. |
444 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 30.87 m | An object of mass 13.09 kg is released from rest at height 30.87 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) = 24.61 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. |
445 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 8.993 m | An object of mass 14.47 kg is released from rest at height 8.993 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) = 13.28 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. |
446 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 9.525 m | An object of mass 9.141 kg is released from rest at height 9.525 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) = 13.67 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. |
447 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 18.41 m | An object of mass 6.911 kg is released from rest at height 18.41 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) = 19 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. |
448 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 4.256 m | An object of mass 8.437 kg is released from rest at height 4.256 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) = 9.136 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. |
449 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 26.77 m | An object of mass 8.65 kg is released from rest at height 26.77 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) = 22.91 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. |
450 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 6.529 m | An object of mass 7.611 kg is released from rest at height 6.529 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) = 11.32 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. |
451 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 3.152 m | An object of mass 18.48 kg is released from rest at height 3.152 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) = 7.862 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. |
452 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 4.183 m | An object of mass 16.67 kg is released from rest at height 4.183 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) = 9.057 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. |
453 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 29.68 m | An object of mass 2.112 kg is released from rest at height 29.68 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) = 24.13 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. |
454 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 22.48 m | An object of mass 16.27 kg is released from rest at height 22.48 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 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. |
455 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 22.68 m | An object of mass 11.81 kg is released from rest at height 22.68 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) = 21.09 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. |
456 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 5.328 m | An object of mass 6.727 kg is released from rest at height 5.328 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) = 10.22 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. |
457 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 26.78 m | An object of mass 7.201 kg is released from rest at height 26.78 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) = 22.92 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. |
458 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 34.79 m | An object of mass 15.06 kg is released from rest at height 34.79 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) = 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. |
459 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 38.75 m | An object of mass 14.48 kg is released from rest at height 38.75 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) = 27.57 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. |
460 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 14.39 m | An object of mass 12.09 kg is released from rest at height 14.39 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) = 16.8 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. |
461 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 8.903 m | An object of mass 11.64 kg is released from rest at height 8.903 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) = 13.21 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. |
462 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 9.358 m | An object of mass 13.2 kg is released from rest at height 9.358 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) = 13.55 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. |
463 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 33.89 m | An object of mass 2.343 kg is released from rest at height 33.89 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. |
464 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 30.62 m | An object of mass 7.478 kg is released from rest at height 30.62 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) = 24.51 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. |
465 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 32.39 m | An object of mass 11.57 kg is released from rest at height 32.39 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) = 25.2 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. |
466 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 38.99 m | An object of mass 16.93 kg is released from rest at height 38.99 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) = 27.66 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. |
467 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 24.74 m | An object of mass 16.4 kg is released from rest at height 24.74 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) = 22.03 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. |
468 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 1.537 m | An object of mass 12.93 kg is released from rest at height 1.537 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) = 5.491 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. |
469 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 33.26 m | An object of mass 18.6 kg is released from rest at height 33.26 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) = 25.54 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. |
470 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 7.626 m | An object of mass 5.495 kg is released from rest at height 7.626 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) = 12.23 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. |
471 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 12.7 m | An object of mass 14.11 kg is released from rest at height 12.7 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) = 15.79 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. |
472 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 0.7412 m | An object of mass 6.929 kg is released from rest at height 0.7412 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) = 3.813 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. |
473 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 22.87 m | An object of mass 17.42 kg is released from rest at height 22.87 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) = 21.18 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. |
474 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 6.104 m | An object of mass 8.136 kg is released from rest at height 6.104 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) = 10.94 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. |
475 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 1.711 m | An object of mass 12.74 kg is released from rest at height 1.711 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) = 5.793 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. |
476 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 37.33 m, speed 9.39 m/s | An object moves in a circle of radius 37.33 m at constant speed 9.39 m/s. The centripetal acceleration has magnitude a_c = v² / r = 2.362 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. |
477 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 21.05 m, speed 14.29 m/s | An object moves in a circle of radius 21.05 m at constant speed 14.29 m/s. The centripetal acceleration has magnitude a_c = v² / r = 9.708 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. |
478 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 18.57 m, speed 29.14 m/s | An object moves in a circle of radius 18.57 m at constant speed 29.14 m/s. The centripetal acceleration has magnitude a_c = v² / r = 45.74 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. |
479 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 38.86 m, speed 23.14 m/s | An object moves in a circle of radius 38.86 m at constant speed 23.14 m/s. The centripetal acceleration has magnitude a_c = v² / r = 13.77 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. |
480 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 4.339 m, speed 3.052 m/s | An object moves in a circle of radius 4.339 m at constant speed 3.052 m/s. The centripetal acceleration has magnitude a_c = v² / r = 2.146 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. |
481 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 7.955 m, speed 25.1 m/s | An object moves in a circle of radius 7.955 m at constant speed 25.1 m/s. The centripetal acceleration has magnitude a_c = v² / r = 79.17 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. |
482 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 33.73 m, speed 11.61 m/s | An object moves in a circle of radius 33.73 m at constant speed 11.61 m/s. The centripetal acceleration has magnitude a_c = v² / r = 3.997 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. |
483 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 33.13 m, speed 19.94 m/s | An object moves in a circle of radius 33.13 m at constant speed 19.94 m/s. The centripetal acceleration has magnitude a_c = v² / r = 12 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. |
484 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 22.16 m, speed 11.65 m/s | An object moves in a circle of radius 22.16 m at constant speed 11.65 m/s. The centripetal acceleration has magnitude a_c = v² / r = 6.129 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. |
485 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 37.77 m, speed 5.439 m/s | An object moves in a circle of radius 37.77 m at constant speed 5.439 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.7832 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. |
486 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 21.55 m, speed 12.05 m/s | An object moves in a circle of radius 21.55 m at constant speed 12.05 m/s. The centripetal acceleration has magnitude a_c = v² / r = 6.733 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. |
487 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 33.96 m, speed 19.98 m/s | An object moves in a circle of radius 33.96 m at constant speed 19.98 m/s. The centripetal acceleration has magnitude a_c = v² / r = 11.75 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. |
488 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 33.39 m, speed 2.771 m/s | An object moves in a circle of radius 33.39 m at constant speed 2.771 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.23 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. |
489 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 19.82 m, speed 24.37 m/s | An object moves in a circle of radius 19.82 m at constant speed 24.37 m/s. The centripetal acceleration has magnitude a_c = v² / r = 29.97 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. |
490 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 0.4836 m, speed 12.76 m/s | An object moves in a circle of radius 0.4836 m at constant speed 12.76 m/s. The centripetal acceleration has magnitude a_c = v² / r = 336.4 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. |
491 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 10.64 m, speed 6.352 m/s | An object moves in a circle of radius 10.64 m at constant speed 6.352 m/s. The centripetal acceleration has magnitude a_c = v² / r = 3.792 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. |
492 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 12.85 m, speed 13.8 m/s | An object moves in a circle of radius 12.85 m at constant speed 13.8 m/s. The centripetal acceleration has magnitude a_c = v² / r = 14.81 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. |
493 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 0.4857 m, speed 30.13 m/s | An object moves in a circle of radius 0.4857 m at constant speed 30.13 m/s. The centripetal acceleration has magnitude a_c = v² / r = 1869 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. |
494 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 8.867 m, speed 15.83 m/s | An object moves in a circle of radius 8.867 m at constant speed 15.83 m/s. The centripetal acceleration has magnitude a_c = v² / r = 28.25 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. |
495 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 35.21 m, speed 20.51 m/s | An object moves in a circle of radius 35.21 m at constant speed 20.51 m/s. The centripetal acceleration has magnitude a_c = v² / r = 11.95 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. |
496 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 41.68 m, speed 32.44 m/s | An object moves in a circle of radius 41.68 m at constant speed 32.44 m/s. The centripetal acceleration has magnitude a_c = v² / r = 25.25 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. |
497 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 3.697 m, speed 34.61 m/s | An object moves in a circle of radius 3.697 m at constant speed 34.61 m/s. The centripetal acceleration has magnitude a_c = v² / r = 324 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. |
498 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 2.211 m, speed 1.731 m/s | An object moves in a circle of radius 2.211 m at constant speed 1.731 m/s. The centripetal acceleration has magnitude a_c = v² / r = 1.355 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. |
499 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 46.07 m, speed 34.62 m/s | An object moves in a circle of radius 46.07 m at constant speed 34.62 m/s. The centripetal acceleration has magnitude a_c = v² / r = 26.02 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. |
500 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 28.83 m, speed 23.36 m/s | An object moves in a circle of radius 28.83 m at constant speed 23.36 m/s. The centripetal acceleration has magnitude a_c = v² / r = 18.93 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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