Work & energy worksheet with answers

Free printable Work & energy worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
m = 1 kggh = 50 m

A 1 kg ball is dropped from rest from a height of 50 m. Ignore air resistance. Find its speed v just before it hits the ground.

m = 1 kgh = 50 mg = 9.81 m/s²
v = m/s
2.Easy
80 kgh = 6 mt = 30 s

A hoist lifts an 80 kg load at constant speed through a height of 6 m in 30 s. Find the average power P it delivers to the load, in W.

m = 80 kgh = 6 mt = 30 sg = 9.81 m/s²
P = W
3.Medium
35°d = 6 mμ = 0.1

A 2 kg block slides 6 m down a slope at 35° to the horizontal, with a coefficient of kinetic friction of 0.1. Find the work Wf done against friction.

m = 2 kgθ = 35°μ = 0.1d = 6 mg = 9.81 m/s²
Wf = J
4.Medium
15°d = 13 mμ = 0.15

A 2 kg block slides 13 m down a slope at 15° to the horizontal, with a coefficient of kinetic friction of 0.15. Find the work Wf done against friction.

m = 2 kgθ = 15°μ = 0.15d = 13 mg = 9.81 m/s²
Wf = J
5.Hard
k = 3000 N/m40°μ = 0.35 kg

A spring of stiffness 3000 N/m at the bottom of a 40° slope is compressed by 15 cm against a 5 kg block and released. The coefficient of kinetic friction between block and slope is 0.3. 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 = 5 kgk = 3000 N/mx = 15 cmθ = 40°μ = 0.3g = 9.81 m/s²
d = m
6.Hard
h = 11.2 mR = 4 mv = ?

A 10 kg cart is released from rest at a height of 11.2 m on a smooth track that leads into a vertical circular loop of radius 4 m. Find the speed v of the cart at the top of the loop.

m = 10 kgh = 11.2 mR = 4 mg = 9.81 m/s²
v = m/s

Answer key

  1. 1. v = 31.32 m/s
  2. 2. P = 157 W
  3. 3. Wf = 9.643 J
  4. 4. Wf = 36.96 J
  5. 5. d = 0.7885 m
  6. 6. v = 7.924 m/s

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