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 240 km/h?
v = 240 km/hamax = 1 m/s²
rmin = m
Circular motion worksheet with answers
2.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
3.Medium
In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.3 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.3. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.
r = 2.3 mμs = 0.3g = 9.81 m/s²
n = rpm
4.Medium
A car takes a flat curve of radius 60 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 = 60 mμs = 0.4g = 9.81 m/s²
vmax = m/s
5.Hard
A 0.6 kg ball on a light string 1.5 m long is swung in a vertical circle. At the lowest point its speed is 9.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.
m = 0.6 kgr = 1.5 mvbottom = 9.5 m/sg = 9.81 m/s²
Ttop = N
6.Hard
A 0.4 kg ball on a string 1.4 m long is swung in a vertical circle. At the lowest point it moves at 4.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.
m = 0.4 kgr = 1.4 mv = 4.5 m/sg = 9.81 m/s²
T = N
Answer key
- 1. rmin = 4444 m
- 2. rmin = 3086 m
- 3. n = 36.01 rpm
- 4. vmax = 15.34 m/s
- 5. Ttop = 6.67 N
- 6. T = 9.71 N
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