1.Easy
For passenger comfort the centripetal acceleration on a railway curve must not exceed 2 m/s². What is the smallest radius rmin for a curve taken at 250 km/h?
v = 250 km/hamax = 2 m/s²
rmin = m
Circular motion worksheet with answers
2.Easy
For passenger comfort the centripetal acceleration on a railway curve must not exceed 2 m/s². What is the smallest radius rmin for a curve taken at 120 km/h?
v = 120 km/hamax = 2 m/s²
rmin = m
3.Medium
A car takes a flat curve of radius 105 m. The coefficient of static friction between tyres and road is 0.8. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.
r = 105 mμs = 0.8g = 9.81 m/s²
vmax = m/s
4.Medium
A 1800 kg car drives over the top of a hump in the road at 6 m/s. The top of the hump is a circular arc of radius 105 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.
m = 1800 kgv = 6 m/sr = 105 mg = 9.81 m/s²
N = N
5.Hard
A curve of radius 150 m is banked at 30°, and the coefficient of static friction between tyres and road is 0.2. 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 = 150 mθ = 30°μs = 0.2g = 9.81 m/s²
vmax = m/s
6.Hard
A 3.5 kg cart is released from rest at a height of 26.1 m on a frictionless track and runs through a vertical loop of radius 9 m. Use g = 9.81 m/s². Find the normal force Nbottom of the track on the cart at the bottom of the loop.
m = 3.5 kgh = 26.1 mR = 9 mg = 9.81 m/s²
Nbottom = N
Answer key
- 1. rmin = 2411 m
- 2. rmin = 555.6 m
- 3. vmax = 28.71 m/s
- 4. N = 17041 N
- 5. vmax = 35.96 m/s
- 6. Nbottom = 233.5 N
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