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 = 36 m

A 1 kg ball is dropped from rest from a height of 36 m. Ignore air resistance. Find its speed v just before it hits the ground.

m = 1 kgh = 36 mg = 9.81 m/s²
v = m/s
2.Easy
F = 90 N45°d = 18 m

A crate is pulled 18 m along a level floor by a rope that makes 45° with the horizontal. The tension in the rope is 90 N. Find the work W done by the rope on the crate.

F = 90 Nd = 18 mθ = 45°
W = J
3.Medium
0.1 kgk = 1500 N/mh = ?

A toy launcher has a vertical spring of stiffness 1500 N/m. A 0.1 kg ball is placed on it and the spring is compressed by 10 cm, then released. Ignoring air resistance and the spring’s mass, find the height h the ball rises, measured from its position when the spring was compressed.

m = 0.1 kgk = 1500 N/mx = 10 cmg = 9.81 m/s²
h = m
4.Medium
40°d = 10 mμ = 0.25

A 0.5 kg block slides 10 m down a slope at 40° to the horizontal, with a coefficient of kinetic friction of 0.25. Find the work Wf done against friction.

m = 0.5 kgθ = 40°μ = 0.25d = 10 mg = 9.81 m/s²
Wf = J
5.Hard
h = 5.3 mR = 1.5 mv = ?

A 5 kg cart is released from rest at a height of 5.3 m on a smooth track that leads into a vertical circular loop of radius 1.5 m. Find the speed v of the cart at the top of the loop.

m = 5 kgh = 5.3 mR = 1.5 mg = 9.81 m/s²
v = m/s
6.Hard
F = 35 N35°μ = 0.32 kg

A 2 kg block starts from rest at the bottom of a 35° slope and is pulled up the slope by a constant force of 35 N parallel to the slope. The coefficient of kinetic friction is 0.3. Find the speed v of the block after it has moved 5 m up the slope.

m = 2 kgF = 35 Nθ = 35°μ = 0.3d = 5 mg = 9.81 m/s²
v = m/s

Answer key

  1. 1. v = 26.58 m/s
  2. 2. W = 1146 J
  3. 3. h = 7.645 m
  4. 4. Wf = 9.394 J
  5. 5. v = 6.718 m/s
  6. 6. v = 9.728 m/s

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