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 240 km/h?
v = 240 km/hamax = 0.5 m/s²
rmin = m
Circular motion worksheet with answers
2.Easy
A 1100 kg car drives around a flat curve of radius 70 m at a constant 16 m/s. Find the inward (centripetal) force Fc needed.
m = 1100 kgv = 16 m/sr = 70 m
Fc = N
3.Medium
A car takes a flat curve of radius 90 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 = 90 mμs = 0.8g = 9.81 m/s²
vmax = m/s
4.Medium
In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.8 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.6. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.
r = 2.8 mμs = 0.6g = 9.81 m/s²
ω = rad/s
5.Hard
A 1.8 kg ball on a light string 0.8 m long is swung in a vertical circle. At the lowest point its speed is 8 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 = 0.8 mvbottom = 8 m/sg = 9.81 m/s²
Ttop = N
6.Hard
A curve of radius 100 m is banked at 30°, and 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 a car can take the curve without sliding up and out.
r = 100 mθ = 30°μs = 0.3g = 9.81 m/s²
vmax = m/s
Answer key
- 1. rmin = 8889 m
- 2. Fc = 4023 N
- 3. vmax = 26.58 m/s
- 4. ω = 2.416 rad/s
- 5. Ttop = 55.71 N
- 6. vmax = 32.26 m/s
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