1.Easy
For passenger comfort the centripetal acceleration on a railway curve must not exceed 1 m/s². What is the smallest radius rmin for a curve taken at 240 km/h?
v = 240 km/hamax = 1 m/s²
rmin = m
Circular motion worksheet with answers
2.Easy
A 1 kg stone is whirled in a horizontal circle of radius 1.2 m on a smooth, level table, held by a string that breaks at a tension of 50 N. Find the highest speed vmax the stone can have.
m = 1 kgr = 1.2 mTmax = 50 N
vmax = m/s
3.Medium
A small ball on a string of length 1.5 m moves in a horizontal circle so that the string makes a constant angle of 50° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.
L = 1.5 mθ = 50°g = 9.81 m/s²
T = s
4.Medium
A road engineer wants cars to take a curve of radius 170 m at 120 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.
r = 170 mv = 120 km/hg = 9.81 m/s²
θ = °
5.Hard
A curve of radius 150 m is banked at 8°, and the coefficient of static friction between tyres and road is 0.4. 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 = 150 mθ = 8°μs = 0.4g = 9.81 m/s²
vmax = m/s
6.Hard
A curve of radius 240 m is banked at 12°, and the coefficient of static friction between tyres and road is 0.4. 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 = 240 mθ = 12°μs = 0.4g = 9.81 m/s²
vmax = m/s
Answer key
- 1. rmin = 4444 m
- 2. vmax = 7.746 m/s
- 3. T = 1.97 s
- 4. θ = 33.67 °
- 5. vmax = 29.03 m/s
- 6. vmax = 39.7 m/s
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