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
2,201
physics
mechanics
mechanical_energy
4
worked_example
Conservation of mechanical energy: drop from height 30.69 m
An object of mass 18.47 kg is released from rest at height 30.69 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) = 24.54 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.
2,202
physics
mechanics
mechanical_energy
4
worked_example
Conservation of mechanical energy: drop from height 4.17 m
An object of mass 11.44 kg is released from rest at height 4.17 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) = 9.044 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.
2,203
physics
mechanics
mechanical_energy
4
worked_example
Conservation of mechanical energy: drop from height 28.09 m
An object of mass 16.09 kg is released from rest at height 28.09 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) = 23.47 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.
2,204
physics
mechanics
mechanical_energy
4
worked_example
Conservation of mechanical energy: drop from height 12.76 m
An object of mass 2.126 kg is released from rest at height 12.76 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) = 15.82 m/s at the reference lev...
K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2
newton_second_law; work-energy theorem
Apply conservation of mechanical energy to free-fall motion.
2,205
physics
mechanics
mechanical_energy
4
worked_example
Conservation of mechanical energy: drop from height 30.78 m
An object of mass 12.96 kg is released from rest at height 30.78 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 24.57 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.
2,206
physics
mechanics
mechanical_energy
4
worked_example
Conservation of mechanical energy: drop from height 37.92 m
An object of mass 9.517 kg is released from rest at height 37.92 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) = 27.27 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.
2,207
physics
mechanics
mechanical_energy
4
worked_example
Conservation of mechanical energy: drop from height 35.88 m
An object of mass 3.046 kg is released from rest at height 35.88 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) = 26.53 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.
2,208
physics
mechanics
mechanical_energy
4
worked_example
Conservation of mechanical energy: drop from height 14.86 m
An object of mass 5.309 kg is released from rest at height 14.86 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 17.07 m/s at the reference lev...
K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2
newton_second_law; work-energy theorem
Apply conservation of mechanical energy to free-fall motion.
2,209
physics
mechanics
mechanical_energy
4
worked_example
Conservation of mechanical energy: drop from height 36.73 m
An object of mass 3.83 kg is released from rest at height 36.73 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) = 26.84 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.
2,210
physics
mechanics
mechanical_energy
4
worked_example
Conservation of mechanical energy: drop from height 34.5 m
An object of mass 6.74 kg is released from rest at height 34.5 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 26.01 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.
2,211
physics
mechanics
mechanical_energy
4
worked_example
Conservation of mechanical energy: drop from height 19.76 m
An object of mass 6.63 kg is released from rest at height 19.76 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) = 19.68 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.
2,212
physics
mechanics
mechanical_energy
4
worked_example
Conservation of mechanical energy: drop from height 4.959 m
An object of mass 1.494 kg is released from rest at height 4.959 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) = 9.862 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.
2,213
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 23.98 m, speed 33.98 m/s
An object moves in a circle of radius 23.98 m at constant speed 33.98 m/s. The centripetal acceleration has magnitude a_c = v² / r = 48.15 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.
2,214
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 14.18 m, speed 14.6 m/s
An object moves in a circle of radius 14.18 m at constant speed 14.6 m/s. The centripetal acceleration has magnitude a_c = v² / r = 15.02 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.
2,215
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 28.78 m, speed 20.81 m/s
An object moves in a circle of radius 28.78 m at constant speed 20.81 m/s. The centripetal acceleration has magnitude a_c = v² / r = 15.05 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.
2,216
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 20.34 m, speed 28.86 m/s
An object moves in a circle of radius 20.34 m at constant speed 28.86 m/s. The centripetal acceleration has magnitude a_c = v² / r = 40.93 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.
2,217
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 5.438 m, speed 22.69 m/s
An object moves in a circle of radius 5.438 m at constant speed 22.69 m/s. The centripetal acceleration has magnitude a_c = v² / r = 94.67 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.
2,218
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 3.639 m, speed 12.78 m/s
An object moves in a circle of radius 3.639 m at constant speed 12.78 m/s. The centripetal acceleration has magnitude a_c = v² / r = 44.9 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.
2,219
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 23.1 m, speed 24.03 m/s
An object moves in a circle of radius 23.1 m at constant speed 24.03 m/s. The centripetal acceleration has magnitude a_c = v² / r = 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.
2,220
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 12 m, speed 10.5 m/s
An object moves in a circle of radius 12 m at constant speed 10.5 m/s. The centripetal acceleration has magnitude a_c = v² / r = 9.191 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.
2,221
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 8.035 m, speed 19.81 m/s
An object moves in a circle of radius 8.035 m at constant speed 19.81 m/s. The centripetal acceleration has magnitude a_c = v² / r = 48.85 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.
2,222
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 3.396 m, speed 9.121 m/s
An object moves in a circle of radius 3.396 m at constant speed 9.121 m/s. The centripetal acceleration has magnitude a_c = v² / r = 24.5 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.
2,223
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 34.73 m, speed 17.81 m/s
An object moves in a circle of radius 34.73 m at constant speed 17.81 m/s. The centripetal acceleration has magnitude a_c = v² / r = 9.137 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.
2,224
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 49.01 m, speed 23.12 m/s
An object moves in a circle of radius 49.01 m at constant speed 23.12 m/s. The centripetal acceleration has magnitude a_c = v² / r = 10.91 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.
2,225
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 17.18 m, speed 28.07 m/s
An object moves in a circle of radius 17.18 m at constant speed 28.07 m/s. The centripetal acceleration has magnitude a_c = v² / r = 45.88 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.
2,226
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 8.737 m, speed 27.11 m/s
An object moves in a circle of radius 8.737 m at constant speed 27.11 m/s. The centripetal acceleration has magnitude a_c = v² / r = 84.15 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.
2,227
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 36.99 m, speed 28.76 m/s
An object moves in a circle of radius 36.99 m at constant speed 28.76 m/s. The centripetal acceleration has magnitude a_c = v² / r = 22.37 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.
2,228
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 41.85 m, speed 5.459 m/s
An object moves in a circle of radius 41.85 m at constant speed 5.459 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.7119 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.
2,229
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 29.84 m, speed 13.69 m/s
An object moves in a circle of radius 29.84 m at constant speed 13.69 m/s. The centripetal acceleration has magnitude a_c = v² / r = 6.28 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.
2,230
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 4.973 m, speed 18.36 m/s
An object moves in a circle of radius 4.973 m at constant speed 18.36 m/s. The centripetal acceleration has magnitude a_c = v² / r = 67.81 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.
2,231
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 15.47 m, speed 16.83 m/s
An object moves in a circle of radius 15.47 m at constant speed 16.83 m/s. The centripetal acceleration has magnitude a_c = v² / r = 18.3 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.
2,232
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 29.95 m, speed 27.73 m/s
An object moves in a circle of radius 29.95 m at constant speed 27.73 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.
2,233
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 29.86 m, speed 32.97 m/s
An object moves in a circle of radius 29.86 m at constant speed 32.97 m/s. The centripetal acceleration has magnitude a_c = v² / r = 36.41 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.
2,234
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 16.44 m, speed 26.15 m/s
An object moves in a circle of radius 16.44 m at constant speed 26.15 m/s. The centripetal acceleration has magnitude a_c = v² / r = 41.62 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.).
a_c = v^2 / r; F_c = m v^2 / r
newton_second_law
Calculate centripetal acceleration and identify the force providing it.
2,235
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 3.168 m, speed 9.487 m/s
An object moves in a circle of radius 3.168 m at constant speed 9.487 m/s. The centripetal acceleration has magnitude a_c = v² / r = 28.41 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.
2,236
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 7.032 m, speed 23.65 m/s
An object moves in a circle of radius 7.032 m at constant speed 23.65 m/s. The centripetal acceleration has magnitude a_c = v² / r = 79.54 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.
2,237
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 37.77 m, speed 32.58 m/s
An object moves in a circle of radius 37.77 m at constant speed 32.58 m/s. The centripetal acceleration has magnitude a_c = v² / r = 28.11 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.
2,238
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 37.88 m, speed 26.77 m/s
An object moves in a circle of radius 37.88 m at constant speed 26.77 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.
2,239
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 22.7 m, speed 12.37 m/s
An object moves in a circle of radius 22.7 m at constant speed 12.37 m/s. The centripetal acceleration has magnitude a_c = v² / r = 6.738 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.
2,240
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 30.82 m, speed 18.44 m/s
An object moves in a circle of radius 30.82 m at constant speed 18.44 m/s. The centripetal acceleration has magnitude a_c = v² / r = 11.03 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.
2,241
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 10.36 m, speed 35.22 m/s
An object moves in a circle of radius 10.36 m at constant speed 35.22 m/s. The centripetal acceleration has magnitude a_c = v² / r = 119.7 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.
2,242
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 15.06 m, speed 31.98 m/s
An object moves in a circle of radius 15.06 m at constant speed 31.98 m/s. The centripetal acceleration has magnitude a_c = v² / r = 67.92 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.
2,243
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 34.01 m, speed 36.82 m/s
An object moves in a circle of radius 34.01 m at constant speed 36.82 m/s. The centripetal acceleration has magnitude a_c = v² / r = 39.87 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.
2,244
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 46.84 m, speed 28.99 m/s
An object moves in a circle of radius 46.84 m at constant speed 28.99 m/s. The centripetal acceleration has magnitude a_c = v² / r = 17.95 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.
2,245
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 45.76 m, speed 39.62 m/s
An object moves in a circle of radius 45.76 m at constant speed 39.62 m/s. The centripetal acceleration has magnitude a_c = v² / r = 34.3 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.
2,246
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 29.18 m, speed 24.85 m/s
An object moves in a circle of radius 29.18 m at constant speed 24.85 m/s. The centripetal acceleration has magnitude a_c = v² / r = 21.16 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.
2,247
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 25.57 m, speed 34.06 m/s
An object moves in a circle of radius 25.57 m at constant speed 34.06 m/s. The centripetal acceleration has magnitude a_c = v² / r = 45.36 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.
2,248
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 42.64 m, speed 3.434 m/s
An object moves in a circle of radius 42.64 m at constant speed 3.434 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.2766 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.
2,249
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 45.06 m, speed 38.75 m/s
An object moves in a circle of radius 45.06 m at constant speed 38.75 m/s. The centripetal acceleration has magnitude a_c = v² / r = 33.32 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.
2,250
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 0.1421 m, speed 22.84 m/s
An object moves in a circle of radius 0.1421 m at constant speed 22.84 m/s. The centripetal acceleration has magnitude a_c = v² / r = 3672 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.
2,251
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 48.94 m, speed 5.278 m/s
An object moves in a circle of radius 48.94 m at constant speed 5.278 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.5693 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.
2,252
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 14.18 m, speed 2.216 m/s
An object moves in a circle of radius 14.18 m at constant speed 2.216 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.3463 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.
2,253
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 21.64 m, speed 24.02 m/s
An object moves in a circle of radius 21.64 m at constant speed 24.02 m/s. The centripetal acceleration has magnitude a_c = v² / r = 26.65 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.
2,254
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 31.3 m, speed 28.76 m/s
An object moves in a circle of radius 31.3 m at constant speed 28.76 m/s. The centripetal acceleration has magnitude a_c = v² / r = 26.43 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.
2,255
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 20.36 m, speed 17.97 m/s
An object moves in a circle of radius 20.36 m at constant speed 17.97 m/s. The centripetal acceleration has magnitude a_c = v² / r = 15.86 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.
2,256
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 10.64 m, speed 7.763 m/s
An object moves in a circle of radius 10.64 m at constant speed 7.763 m/s. The centripetal acceleration has magnitude a_c = v² / r = 5.664 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.
2,257
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 7.04 m, speed 22.66 m/s
An object moves in a circle of radius 7.04 m at constant speed 22.66 m/s. The centripetal acceleration has magnitude a_c = v² / r = 72.95 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.
2,258
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 42.18 m, speed 15.05 m/s
An object moves in a circle of radius 42.18 m at constant speed 15.05 m/s. The centripetal acceleration has magnitude a_c = v² / r = 5.371 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.
2,259
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 20.92 m, speed 12.25 m/s
An object moves in a circle of radius 20.92 m at constant speed 12.25 m/s. The centripetal acceleration has magnitude a_c = v² / r = 7.174 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.
2,260
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 43.65 m, speed 5.896 m/s
An object moves in a circle of radius 43.65 m at constant speed 5.896 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.7965 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.
2,261
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 0.679 m, speed 26.29 m/s
An object moves in a circle of radius 0.679 m at constant speed 26.29 m/s. The centripetal acceleration has magnitude a_c = v² / r = 1018 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.
2,262
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 7.285 m, speed 35.51 m/s
An object moves in a circle of radius 7.285 m at constant speed 35.51 m/s. The centripetal acceleration has magnitude a_c = v² / r = 173.1 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.
2,263
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 32.93 m, speed 39.02 m/s
An object moves in a circle of radius 32.93 m at constant speed 39.02 m/s. The centripetal acceleration has magnitude a_c = v² / r = 46.25 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.
2,264
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 6.875 m, speed 6.352 m/s
An object moves in a circle of radius 6.875 m at constant speed 6.352 m/s. The centripetal acceleration has magnitude a_c = v² / r = 5.868 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.
2,265
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 40.32 m, speed 34.55 m/s
An object moves in a circle of radius 40.32 m at constant speed 34.55 m/s. The centripetal acceleration has magnitude a_c = v² / r = 29.6 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.
2,266
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 44.69 m, speed 28.12 m/s
An object moves in a circle of radius 44.69 m at constant speed 28.12 m/s. The centripetal acceleration has magnitude a_c = v² / r = 17.69 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.
2,267
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 46.52 m, speed 25.31 m/s
An object moves in a circle of radius 46.52 m at constant speed 25.31 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.
2,268
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 22.77 m, speed 17.54 m/s
An object moves in a circle of radius 22.77 m at constant speed 17.54 m/s. The centripetal acceleration has magnitude a_c = v² / r = 13.51 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.
2,269
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 41.02 m, speed 16 m/s
An object moves in a circle of radius 41.02 m at constant speed 16 m/s. The centripetal acceleration has magnitude a_c = v² / r = 6.244 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.
2,270
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 11.36 m, speed 17.57 m/s
An object moves in a circle of radius 11.36 m at constant speed 17.57 m/s. The centripetal acceleration has magnitude a_c = v² / r = 27.15 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.
2,271
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 0.4708 m, speed 20.43 m/s
An object moves in a circle of radius 0.4708 m at constant speed 20.43 m/s. The centripetal acceleration has magnitude a_c = v² / r = 886.5 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.
2,272
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 36.57 m, speed 28.77 m/s
An object moves in a circle of radius 36.57 m at constant speed 28.77 m/s. The centripetal acceleration has magnitude a_c = v² / r = 22.64 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.
2,273
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 13.54 m, speed 37.14 m/s
An object moves in a circle of radius 13.54 m at constant speed 37.14 m/s. The centripetal acceleration has magnitude a_c = v² / r = 101.9 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.
2,274
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 28.86 m, speed 2.305 m/s
An object moves in a circle of radius 28.86 m at constant speed 2.305 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.1841 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.
2,275
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 1.989 m, speed 19.85 m/s
An object moves in a circle of radius 1.989 m at constant speed 19.85 m/s. The centripetal acceleration has magnitude a_c = v² / r = 198 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.
2,276
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 18.49 m, speed 23.63 m/s
An object moves in a circle of radius 18.49 m at constant speed 23.63 m/s. The centripetal acceleration has magnitude a_c = v² / r = 30.2 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.
2,277
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 48.09 m, speed 4.122 m/s
An object moves in a circle of radius 48.09 m at constant speed 4.122 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.3534 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.
2,278
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 36.54 m, speed 21.53 m/s
An object moves in a circle of radius 36.54 m at constant speed 21.53 m/s. The centripetal acceleration has magnitude a_c = v² / r = 12.69 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.
2,279
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 42.98 m, speed 30.27 m/s
An object moves in a circle of radius 42.98 m at constant speed 30.27 m/s. The centripetal acceleration has magnitude a_c = v² / r = 21.32 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.
2,280
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 14.04 m, speed 21.16 m/s
An object moves in a circle of radius 14.04 m at constant speed 21.16 m/s. The centripetal acceleration has magnitude a_c = v² / r = 31.89 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.
2,281
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 26.22 m, speed 24.79 m/s
An object moves in a circle of radius 26.22 m at constant speed 24.79 m/s. The centripetal acceleration has magnitude a_c = v² / r = 23.45 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.
2,282
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 12.34 m, speed 25.6 m/s
An object moves in a circle of radius 12.34 m at constant speed 25.6 m/s. The centripetal acceleration has magnitude a_c = v² / r = 53.1 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.
2,283
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 33.22 m, speed 27.08 m/s
An object moves in a circle of radius 33.22 m at constant speed 27.08 m/s. The centripetal acceleration has magnitude a_c = v² / r = 22.07 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.).
a_c = v^2 / r; F_c = m v^2 / r
newton_second_law
Calculate centripetal acceleration and identify the force providing it.
2,284
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 34.24 m, speed 22.03 m/s
An object moves in a circle of radius 34.24 m at constant speed 22.03 m/s. The centripetal acceleration has magnitude a_c = v² / r = 14.17 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.
2,285
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 29.02 m, speed 24.91 m/s
An object moves in a circle of radius 29.02 m at constant speed 24.91 m/s. The centripetal acceleration has magnitude a_c = v² / r = 21.38 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.
2,286
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 45.19 m, speed 21.87 m/s
An object moves in a circle of radius 45.19 m at constant speed 21.87 m/s. The centripetal acceleration has magnitude a_c = v² / r = 10.58 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.
2,287
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 0.6381 m, speed 18.71 m/s
An object moves in a circle of radius 0.6381 m at constant speed 18.71 m/s. The centripetal acceleration has magnitude a_c = v² / r = 548.5 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.
2,288
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 45.31 m, speed 23.38 m/s
An object moves in a circle of radius 45.31 m at constant speed 23.38 m/s. The centripetal acceleration has magnitude a_c = v² / r = 12.07 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.).
a_c = v^2 / r; F_c = m v^2 / r
newton_second_law
Calculate centripetal acceleration and identify the force providing it.
2,289
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 16.64 m, speed 14.76 m/s
An object moves in a circle of radius 16.64 m at constant speed 14.76 m/s. The centripetal acceleration has magnitude a_c = v² / r = 13.1 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.
2,290
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 48.89 m, speed 12.49 m/s
An object moves in a circle of radius 48.89 m at constant speed 12.49 m/s. The centripetal acceleration has magnitude a_c = v² / r = 3.191 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.
2,291
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 8.459 m, speed 28.11 m/s
An object moves in a circle of radius 8.459 m at constant speed 28.11 m/s. The centripetal acceleration has magnitude a_c = v² / r = 93.4 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.
2,292
physics
mechanics
uniform_circular_motion
5
worked_example
Centripetal acceleration: radius 29.92 m, speed 12.86 m/s
An object moves in a circle of radius 29.92 m at constant speed 12.86 m/s. The centripetal acceleration has magnitude a_c = v² / r = 5.526 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.
2,293
physics
electromagnetism
coulomb_law
5
worked_example
Coulomb force between charges 6.2356e-05 C and 5.7856e-04 C separated by 1.15 m
Two point charges q1 = 6.2356e-05 C and q2 = 5.7856e-04 C are separated by distance r = 1.15 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 245.2 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite.
F = k |q1 q2| / r^2; k = 1/(4 π ε_0)
newton_second_law
Compute the Coulomb force between two point charges.
2,294
physics
electromagnetism
coulomb_law
5
worked_example
Coulomb force between charges 8.0909e-04 C and -2.8753e-04 C separated by 0.1742 m
Two point charges q1 = 8.0909e-04 C and q2 = -2.8753e-04 C are separated by distance r = 0.1742 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 6.8904e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite.
F = k |q1 q2| / r^2; k = 1/(4 π ε_0)
newton_second_law
Compute the Coulomb force between two point charges.
2,295
physics
electromagnetism
coulomb_law
5
worked_example
Coulomb force between charges -8.5159e-04 C and 2.5280e-04 C separated by 1.235 m
Two point charges q1 = -8.5159e-04 C and q2 = 2.5280e-04 C are separated by distance r = 1.235 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1268 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite.
F = k |q1 q2| / r^2; k = 1/(4 π ε_0)
newton_second_law
Compute the Coulomb force between two point charges.
2,296
physics
electromagnetism
coulomb_law
5
worked_example
Coulomb force between charges 8.5800e-04 C and -7.4169e-04 C separated by 1.212 m
Two point charges q1 = 8.5800e-04 C and q2 = -7.4169e-04 C are separated by distance r = 1.212 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3896 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite.
F = k |q1 q2| / r^2; k = 1/(4 π ε_0)
newton_second_law
Compute the Coulomb force between two point charges.
2,297
physics
electromagnetism
coulomb_law
5
worked_example
Coulomb force between charges -6.5950e-04 C and 8.0803e-04 C separated by 0.5299 m
Two point charges q1 = -6.5950e-04 C and q2 = 8.0803e-04 C are separated by distance r = 0.5299 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.7057e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite.
F = k |q1 q2| / r^2; k = 1/(4 π ε_0)
newton_second_law
Compute the Coulomb force between two point charges.
2,298
physics
electromagnetism
coulomb_law
5
worked_example
Coulomb force between charges -4.8543e-04 C and -3.4351e-04 C separated by 0.178 m
Two point charges q1 = -4.8543e-04 C and q2 = -3.4351e-04 C are separated by distance r = 0.178 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 4.7322e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite.
F = k |q1 q2| / r^2; k = 1/(4 π ε_0)
newton_second_law
Compute the Coulomb force between two point charges.
2,299
physics
electromagnetism
coulomb_law
5
worked_example
Coulomb force between charges -5.9595e-04 C and -8.3778e-04 C separated by 1.508 m
Two point charges q1 = -5.9595e-04 C and q2 = -8.3778e-04 C are separated by distance r = 1.508 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1973 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite.
F = k |q1 q2| / r^2; k = 1/(4 π ε_0)
newton_second_law
Compute the Coulomb force between two point charges.
2,300
physics
electromagnetism
coulomb_law
5
worked_example
Coulomb force between charges 7.7060e-04 C and -6.6101e-04 C separated by 1.455 m
Two point charges q1 = 7.7060e-04 C and q2 = -6.6101e-04 C are separated by distance r = 1.455 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2163 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite.
F = k |q1 q2| / r^2; k = 1/(4 π ε_0)
newton_second_law
Compute the Coulomb force between two point charges.