1.Easy
A 0.9 kg stone is whirled in a horizontal circle of radius 0.6 m on a smooth, level table, held by a string that breaks at a tension of 90 N. Find the highest speed vmax the stone can have.
m = 0.9 kgr = 0.6 mTmax = 90 N
vmax = m/s
Circular motion worksheet with answers
2.Easy
A 900 kg car drives around a flat curve of radius 130 m at a constant 21 m/s. Find its centripetal acceleration ac.
m = 900 kgv = 21 m/sr = 130 m
ac = m/s²
3.Medium
A car takes a flat curve of radius 130 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.
r = 130 mμs = 0.6g = 9.81 m/s²
vmax = m/s
4.Medium
A car drives over the top of a hump in the road, which is a circular arc of radius 85 m. Use g = 9.81 m/s². Above what speed vmax do the wheels leave the road at the top?
r = 85 mg = 9.81 m/s²
vmax = m/s
5.Hard
A curve of radius 90 m is banked at 25°, and the coefficient of static friction between tyres and road is 0.15. Use g = 9.81 m/s². Find the highest speed vmax at which a car can take the curve without sliding up and out.
r = 90 mθ = 25°μs = 0.15g = 9.81 m/s²
vmax = m/s
6.Hard
A 3.5 kg cart is released from rest at a height of 37.5 m on a frictionless track and runs through a vertical loop of radius 7.5 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 = 3.5 kgh = 37.5 mR = 7.5 mg = 9.81 m/s²
Nbottom = N
Answer key
- 1. vmax = 7.746 m/s
- 2. ac = 3.392 m/s²
- 3. vmax = 27.66 m/s
- 4. vmax = 28.88 m/s
- 5. vmax = 24.19 m/s
- 6. Nbottom = 377.7 N
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