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 1000 kg car drives around a flat curve of radius 110 m at a constant 22 m/s. Find the inward (centripetal) force Fc needed.
m = 1000 kgv = 22 m/sr = 110 m
Fc = N
3.Medium
An 800 kg car drives over the top of a hump in the road at 28 m/s. The top of the hump is a circular arc of radius 100 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.
m = 800 kgv = 28 m/sr = 100 mg = 9.81 m/s²
N = N
4.Medium
In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.5 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 = 3.5 mμs = 0.8g = 9.81 m/s²
ω = rad/s
5.Hard
A 1 kg ball on a string 0.8 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 kgr = 0.8 mv = 4.5 m/sg = 9.81 m/s²
T = N
6.Hard
A curve of radius 280 m is banked at 12°, 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 = 280 mθ = 12°μs = 0.3g = 9.81 m/s²
vmax = m/s
Answer key
- 1. rmin = 3951 m
- 2. Fc = 4400 N
- 3. N = 1576 N
- 4. ω = 1.872 rad/s
- 5. T = 35.12 N
- 6. vmax = 38.78 m/s
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