1.Easy
A 1.7 kg stone is whirled in a horizontal circle of radius 1.4 m on a smooth, level table, held by a string that breaks at a tension of 130 N. Find the highest speed vmax the stone can have.
m = 1.7 kgr = 1.4 mTmax = 130 N
vmax = m/s
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 250 km/h?
v = 250 km/hamax = 0.5 m/s²
rmin = m
3.Medium
A small ball on a string of length 2 m moves in a horizontal circle so that the string makes a constant angle of 45° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.
L = 2 mθ = 45°g = 9.81 m/s²
T = s
4.Medium
A car takes a flat curve of radius 70 m. 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 the car can take the curve without skidding.
r = 70 mμs = 0.3g = 9.81 m/s²
vmax = m/s
5.Hard
A 0.2 kg ball on a string 0.8 m long is swung in a vertical circle. At the lowest point it moves at 7 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.
m = 0.2 kgr = 0.8 mv = 7 m/sg = 9.81 m/s²
T = N
6.Hard
A 1.3 kg ball on a string 1.4 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 = 1.3 kgr = 1.4 mv = 5 m/sg = 9.81 m/s²
T = N
Answer key
- 1. vmax = 10.35 m/s
- 2. rmin = 9645 m
- 3. T = 2.386 s
- 4. vmax = 14.35 m/s
- 5. T = 14.21 N
- 6. T = 35.97 N
Full step-by-step solutions: practise this topic on examproblems.com.