1.Easy
A 0.9 kg stone is whirled in a horizontal circle of radius 1.9 m on a smooth, level table, held by a string that breaks at a tension of 50 N. Find the highest speed vmax the stone can have.
m = 0.9 kgr = 1.9 mTmax = 50 N
vmax = m/s
Circular motion worksheet with answers
2.Easy
An 800 kg car drives around a flat curve of radius 50 m at a constant 10 m/s. Find the inward (centripetal) force Fc needed.
m = 800 kgv = 10 m/sr = 50 m
Fc = N
3.Medium
A car takes a flat curve of radius 30 m. The coefficient of static friction between tyres and road is 0.8. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.
r = 30 mμs = 0.8g = 9.81 m/s²
vmax = m/s
4.Medium
A small ball on a string of length 1.4 m moves in a horizontal circle so that the string makes a constant angle of 20° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.
L = 1.4 mθ = 20°g = 9.81 m/s²
T = s
5.Hard
A curve of radius 40 m is banked at 15°, and the coefficient of static friction between tyres and road is 0.1. Use g = 9.81 m/s². Find the lowest speed vmin at which a car can take the curve without sliding down the bank.
r = 40 mθ = 15°μs = 0.1g = 9.81 m/s²
vmin = m/s
6.Hard
A 4 kg cart is released from rest at a height of 7.75 m on a frictionless track and runs through a vertical loop of radius 2.5 m. Use g = 9.81 m/s². Find the normal force Nbottom of the track on the cart at the bottom of the loop.
m = 4 kgh = 7.75 mR = 2.5 mg = 9.81 m/s²
Nbottom = N
Answer key
- 1. vmax = 10.27 m/s
- 2. Fc = 1600 N
- 3. vmax = 15.34 m/s
- 4. T = 2.301 s
- 5. vmin = 8.011 m/s
- 6. Nbottom = 282.5 N
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