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 160 km/h?
v = 160 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 200 km/h?
v = 200 km/hamax = 1 m/s²
rmin = m
3.Medium
A car drives over the top of a hump in the road, which is a circular arc of radius 110 m. Use g = 9.81 m/s². Above what speed vmax do the wheels leave the road at the top?
r = 110 mg = 9.81 m/s²
vmax = m/s
4.Medium
A 1700 kg car drives over the top of a hump in the road at 26 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 = 1700 kgv = 26 m/sr = 105 mg = 9.81 m/s²
N = N
5.Hard
A curve of radius 80 m is banked at 8°, and 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 a car can take the curve without sliding up and out.
r = 80 mθ = 8°μs = 0.4g = 9.81 m/s²
vmax = m/s
6.Hard
A curve of radius 230 m is banked at 18°, and the coefficient of static friction between tyres and road is 0.1. 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 = 230 mθ = 18°μs = 0.1g = 9.81 m/s²
vmax = m/s
Answer key
- 1. rmin = 1317 m
- 2. rmin = 3086 m
- 3. vmax = 32.85 m/s
- 4. N = 5732 N
- 5. vmax = 21.2 m/s
- 6. vmax = 31.48 m/s
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