1.Easy
A 0.8 kg stone is whirled in a horizontal circle of radius 0.8 m on a smooth, level table, held by a string that breaks at a tension of 10 N. Find the highest speed vmax the stone can have.
m = 0.8 kgr = 0.8 mTmax = 10 N
vmax = m/s
Circular motion worksheet with answers
2.Easy
A 600 kg car drives around a flat curve of radius 80 m at a constant 30 m/s. Find its centripetal acceleration ac.
m = 600 kgv = 30 m/sr = 80 m
ac = m/s²
3.Medium
A small ball on a string of length 1 m moves in a horizontal circle so that the string makes a constant angle of 15° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.
L = 1 mθ = 15°g = 9.81 m/s²
v = m/s
4.Medium
A car takes a flat curve of radius 40 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.
r = 40 mμs = 0.6g = 9.81 m/s²
vmax = m/s
5.Hard
A 1.5 kg ball on a light string 0.5 m long is swung in a vertical circle. At the lowest point its speed is 6 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.
m = 1.5 kgr = 0.5 mvbottom = 6 m/sg = 9.81 m/s²
Ttop = N
6.Hard
A curve of radius 150 m is banked at 10°, 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 = 150 mθ = 10°μs = 0.25g = 9.81 m/s²
vmax = m/s
Answer key
- 1. vmax = 3.162 m/s
- 2. ac = 11.25 m/s²
- 3. v = 0.8248 m/s
- 4. vmax = 15.34 m/s
- 5. Ttop = 34.42 N
- 6. vmax = 25.62 m/s
Full step-by-step solutions: practise this topic on examproblems.com.