1.Easy
A 2.5 kg ball is dropped from rest from a height of 40 m. Ignore air resistance. Find its speed v just before it hits the ground.
m = 2.5 kgh = 40 mg = 9.81 m/s²
v = m/s
Work & energy worksheet with answers
2.Easy
A small ball hangs on a light string of length 0.5 m. It is pulled aside until the string makes 50° with the vertical and released from rest. Ignoring air resistance, find its speed v at the lowest point.
L = 0.5 mθ = 50°g = 9.81 m/s²
v = m/s
3.Medium
A 2 kg block slides 10 m down a slope at 30° to the horizontal, with a coefficient of kinetic friction of 0.35. Find the work Wf done against friction.
m = 2 kgθ = 30°μ = 0.35d = 10 mg = 9.81 m/s²
Wf = J
4.Medium
A car travelling at 110 km/h on a level road brakes hard and skids to a stop with its wheels locked. The coefficient of kinetic friction between the tyres and the road is 0.8. Find the stopping distance d.
v = 110 km/hμ = 0.8g = 9.81 m/s²
d = m
5.Hard
A spring of stiffness 1000 N/m at the bottom of a 15° slope is compressed by 15 cm against a 2 kg block and released. The coefficient of kinetic friction between block and slope is 0.25. How far d up the slope does the block travel from the release point before it stops? (Ignore the short distance over which the spring pushes, i.e. take friction and gravity over the whole distance d.)
m = 2 kgk = 1000 N/mx = 15 cmθ = 15°μ = 0.25g = 9.81 m/s²
d = m
6.Hard
A spring of stiffness 3000 N/m at the bottom of a 20° slope is compressed by 10 cm against a 1 kg block and released. The coefficient of kinetic friction between block and slope is 0.15. How far d up the slope does the block travel from the release point before it stops? (Ignore the short distance over which the spring pushes, i.e. take friction and gravity over the whole distance d.)
m = 1 kgk = 3000 N/mx = 10 cmθ = 20°μ = 0.15g = 9.81 m/s²
d = m
Answer key
- 1. v = 28.01 m/s
- 2. v = 1.872 m/s
- 3. Wf = 59.47 J
- 4. d = 59.48 m
- 5. d = 1.146 m
- 6. d = 3.166 m
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