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 160 km/h?
v = 160 km/hamax = 0.5 m/s²
rmin = m
Circular motion worksheet with answers
2.Easy
A 600 kg car drives around a flat curve of radius 90 m at a constant 15 m/s. Find the inward (centripetal) force Fc needed.
m = 600 kgv = 15 m/sr = 90 m
Fc = N
3.Medium
A 1000 kg car drives over the top of a hump in the road at 12 m/s. The top of the hump is a circular arc of radius 30 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.
m = 1000 kgv = 12 m/sr = 30 mg = 9.81 m/s²
N = N
4.Medium
A car takes a flat curve of radius 20 m. The coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.
r = 20 mμs = 0.3g = 9.81 m/s²
vmax = m/s
5.Hard
A 1.8 kg ball on a light string 1.3 m long is swung in a vertical circle. At the lowest point its speed is 11.5 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 = 1.3 mvbottom = 11.5 m/sg = 9.81 m/s²
Ttop = N
6.Hard
A 1.9 kg ball on a light string 0.6 m long is swung in a vertical circle. At the lowest point its speed is 7.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.
m = 1.9 kgr = 0.6 mvbottom = 7.5 m/sg = 9.81 m/s²
Ttop = N
Answer key
- 1. rmin = 3951 m
- 2. Fc = 1500 N
- 3. N = 5010 N
- 4. vmax = 7.672 m/s
- 5. Ttop = 94.83 N
- 6. Ttop = 84.93 N
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