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 200 km/h?
v = 200 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 0.5 m/s². What is the smallest radius rmin for a curve taken at 160 km/h?
v = 160 km/hamax = 0.5 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 90 m. Use g = 9.81 m/s². Above what speed vmax do the wheels leave the road at the top?
r = 90 mg = 9.81 m/s²
vmax = m/s
4.Medium
In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 1.5 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.8. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.
r = 1.5 mμs = 0.8g = 9.81 m/s²
ω = rad/s
5.Hard
A 0.7 kg ball on a string 0.5 m long is swung in a vertical circle. At the lowest point it moves at 5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.
m = 0.7 kgr = 0.5 mv = 5 m/sg = 9.81 m/s²
T = N
6.Hard
A 0.5 kg ball on a light string 0.6 m long is swung in a vertical circle. At the lowest point its speed is 11 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.
m = 0.5 kgr = 0.6 mvbottom = 11 m/sg = 9.81 m/s²
Ttop = N
Answer key
- 1. rmin = 2058 m
- 2. rmin = 3951 m
- 3. vmax = 29.71 m/s
- 4. ω = 2.859 rad/s
- 5. T = 41.87 N
- 6. Ttop = 76.31 N
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