1.Easy
A 0.7 kg stone is whirled in a horizontal circle of radius 1 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 = 0.7 kgr = 1 mTmax = 90 N
vmax = m/s
Circular motion worksheet with answers
2.Easy
A 1400 kg car drives around a flat curve of radius 40 m at a constant 15 m/s. Find the inward (centripetal) force Fc needed.
m = 1400 kgv = 15 m/sr = 40 m
Fc = N
3.Medium
A car takes a flat curve of radius 110 m. The coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.
r = 110 mμs = 0.3g = 9.81 m/s²
vmax = m/s
4.Medium
A 1300 kg car drives over the top of a hump in the road at 21 m/s. The top of the hump is a circular arc of radius 70 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.
m = 1300 kgv = 21 m/sr = 70 mg = 9.81 m/s²
N = N
5.Hard
A ball on a string 1.5 m long is swung in a vertical circle. Use g = 9.81 m/s². What is the smallest speed vmin at the top for which the string just stays tight?
r = 1.5 mg = 9.81 m/s²
vmin = m/s
6.Hard
A 0.2 kg ball on a light string 1.1 m long is swung in a vertical circle. At the lowest point its speed is 8.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.
m = 0.2 kgr = 1.1 mvbottom = 8.5 m/sg = 9.81 m/s²
Ttop = N
Answer key
- 1. vmax = 11.34 m/s
- 2. Fc = 7875 N
- 3. vmax = 17.99 m/s
- 4. N = 4563 N
- 5. vmin = 3.836 m/s
- 6. Ttop = 3.326 N
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