1.Easy
For passenger comfort the centripetal acceleration on a railway curve must not exceed 1 m/s². What is the smallest radius rmin for a curve taken at 200 km/h?
v = 200 km/hamax = 1 m/s²
rmin = m
Circular motion worksheet with answers
2.Easy
A 1.8 kg stone is whirled in a horizontal circle of radius 1.3 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 = 1.8 kgr = 1.3 mTmax = 90 N
vmax = m/s
3.Medium
A car takes a flat curve of radius 115 m. The coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.
r = 115 mμs = 0.4g = 9.81 m/s²
vmax = m/s
4.Medium
A car takes a flat curve of radius 140 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 = 140 mμs = 0.6g = 9.81 m/s²
vmax = m/s
5.Hard
A 0.9 kg ball on a string 1.4 m long is swung in a vertical circle. At the lowest point it moves at 4 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.
m = 0.9 kgr = 1.4 mv = 4 m/sg = 9.81 m/s²
T = N
6.Hard
A ball on a string 0.9 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 = 0.9 mg = 9.81 m/s²
vmin = m/s
Answer key
- 1. rmin = 3086 m
- 2. vmax = 8.062 m/s
- 3. vmax = 21.24 m/s
- 4. vmax = 28.71 m/s
- 5. T = 19.11 N
- 6. vmin = 2.971 m/s
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