1.Easy
A 0.9 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 70 N. Find the highest speed vmax the stone can have.
m = 0.9 kgr = 1 mTmax = 70 N
vmax = m/s
Circular motion worksheet with answers
2.Easy
An 800 kg car drives around a flat curve of radius 110 m at a constant 27 m/s. Find the inward (centripetal) force Fc needed.
m = 800 kgv = 27 m/sr = 110 m
Fc = N
3.Medium
A car takes a flat curve of radius 100 m. The coefficient of static friction between tyres and road is 0.7. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.
r = 100 mμs = 0.7g = 9.81 m/s²
vmax = m/s
4.Medium
A curve of radius 140 m is banked at 10°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².
r = 140 mθ = 10°g = 9.81 m/s²
v = m/s
5.Hard
A 1.6 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 = 1.6 kgr = 1.1 mvbottom = 8.5 m/sg = 9.81 m/s²
Ttop = N
6.Hard
A curve of radius 190 m is banked at 15°, 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 = 190 mθ = 15°μs = 0.15g = 9.81 m/s²
vmax = m/s
Answer key
- 1. vmax = 8.819 m/s
- 2. Fc = 5302 N
- 3. vmax = 26.2 m/s
- 4. v = 15.56 m/s
- 5. Ttop = 26.61 N
- 6. vmax = 28.49 m/s
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