1.Easy
For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.5 m/s². What is the smallest radius rmin for a curve taken at 240 km/h?
v = 240 km/hamax = 0.5 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 240 km/h?
v = 240 km/hamax = 1 m/s²
rmin = m
3.Medium
A 1800 kg car drives over the top of a hump in the road at 25 m/s. The top of the hump is a circular arc of radius 115 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.
m = 1800 kgv = 25 m/sr = 115 mg = 9.81 m/s²
N = N
4.Medium
A car takes a flat curve of radius 85 m. The coefficient of static friction between tyres and road is 0.5. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.
r = 85 mμs = 0.5g = 9.81 m/s²
vmax = m/s
5.Hard
A curve of radius 270 m is banked at 25°, and the coefficient of static friction between tyres and road is 0.25. 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 = 270 mθ = 25°μs = 0.25g = 9.81 m/s²
vmax = m/s
6.Hard
A 1.6 kg ball on a string 0.8 m long is swung in a vertical circle. At the lowest point it moves at 5.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.
m = 1.6 kgr = 0.8 mv = 5.5 m/sg = 9.81 m/s²
T = N
Answer key
- 1. rmin = 8889 m
- 2. rmin = 4444 m
- 3. N = 7875 N
- 4. vmax = 20.42 m/s
- 5. vmax = 46.34 m/s
- 6. T = 76.2 N
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