1.Easy
For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.5 m/s². What is the smallest radius rmin for a curve taken at 250 km/h?
v = 250 km/hamax = 1.5 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 120 km/h?
v = 120 km/hamax = 1 m/s²
rmin = m
3.Medium
A car takes a flat curve of radius 85 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 = 85 mμs = 0.8g = 9.81 m/s²
vmax = m/s
4.Medium
A car takes a flat curve of radius 115 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 = 115 mμs = 0.5g = 9.81 m/s²
vmax = m/s
5.Hard
A 0.5 kg cart is released from rest at a height of 23.4 m on a frictionless track and runs through a vertical loop of radius 6 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 = 0.5 kgh = 23.4 mR = 6 mg = 9.81 m/s²
Nbottom = N
6.Hard
A 1.8 kg ball on a light string 1.2 m long is swung in a vertical circle. At the lowest point its speed is 9 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.
m = 1.8 kgr = 1.2 mvbottom = 9 m/sg = 9.81 m/s²
Ttop = N
Answer key
- 1. rmin = 3215 m
- 2. rmin = 1111 m
- 3. vmax = 25.83 m/s
- 4. vmax = 23.75 m/s
- 5. Nbottom = 43.16 N
- 6. Ttop = 33.21 N
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