1.Easy
A 1500 kg car drives around a flat curve of radius 200 m at a constant 8 m/s. Find the inward (centripetal) force Fc needed.
m = 1500 kgv = 8 m/sr = 200 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 200 km/h?
v = 200 km/hamax = 0.5 m/s²
rmin = m
3.Medium
A car takes a flat curve of radius 100 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 = 100 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 3.9 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 rotation rate n in revolutions per minute.
r = 3.9 mμs = 0.6g = 9.81 m/s²
n = rpm
5.Hard
A 1.4 kg ball on a string 0.9 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 = 1.4 kgr = 0.9 mv = 5 m/sg = 9.81 m/s²
T = N
6.Hard
A 1.4 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 = 1.4 kgr = 0.6 mvbottom = 11 m/sg = 9.81 m/s²
Ttop = N
Answer key
- 1. Fc = 480 N
- 2. rmin = 6173 m
- 3. vmax = 28.01 m/s
- 4. n = 19.55 rpm
- 5. T = 52.62 N
- 6. Ttop = 213.7 N
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