1.Easy
A 1200 kg car drives around a flat curve of radius 130 m at a constant 18 m/s. Find the inward (centripetal) force Fc needed.
m = 1200 kgv = 18 m/sr = 130 m
Fc = N
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 120 km/h?
v = 120 km/hamax = 0.5 m/s²
rmin = m
3.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 0.3. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.
r = 2.8 mμs = 0.3g = 9.81 m/s²
n = rpm
4.Medium
A car takes a flat curve of radius 145 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 = 145 mμs = 0.8g = 9.81 m/s²
vmax = m/s
5.Hard
A 1.2 kg ball on a string 0.9 m long is swung in a vertical circle. At the lowest point it moves at 4.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.
m = 1.2 kgr = 0.9 mv = 4.5 m/sg = 9.81 m/s²
T = N
6.Hard
A curve of radius 40 m is banked at 30°, and the coefficient of static friction between tyres and road is 0.25. 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 = 40 mθ = 30°μs = 0.25g = 9.81 m/s²
vmax = m/s
Answer key
- 1. Fc = 2991 N
- 2. rmin = 2222 m
- 3. n = 32.63 rpm
- 4. vmax = 33.73 m/s
- 5. T = 38.77 N
- 6. vmax = 19.48 m/s
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