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 = 4 kggh = 31 m

A 4 kg ball is dropped from rest from a height of 31 m. Ignore air resistance. Find its speed v just before it hits the ground.

m = 4 kgh = 31 mg = 9.81 m/s²
v = m/s
2.Easy
F = 60 N60°d = 16 m

A crate is pulled 16 m along a level floor by a rope that makes 60° with the horizontal. The tension in the rope is 60 N. Find the work W done by the rope on the crate.

F = 60 Nd = 16 mθ = 60°
W = J
3.Medium
35°d = 19 mμ = 0.2

A 2.5 kg block slides 19 m down a slope at 35° to the horizontal, with a coefficient of kinetic friction of 0.2. Find the work Wf done against friction.

m = 2.5 kgθ = 35°μ = 0.2d = 19 mg = 9.81 m/s²
Wf = J
4.Medium
90 km/h4°1500 kg

A 1500 kg car drives up a 4° slope at a constant 90 km/h. Air resistance and rolling resistance together amount to 450 N. Find the power P the wheels must deliver, in kW.

m = 1500 kgθ = 4°Fr = 450 Nv = 90 km/hg = 9.81 m/s²
P = kW
5.Hard
3 kg3 kgμ = 0.3d = 1.5 m

A 3 kg block rests on a rough horizontal table (μ = 0.3). A light string runs from it over a smooth pulley at the edge of the table to a hanging 3 kg block. The system is released from rest. Find the speed v of the blocks after the hanging block has dropped 1.5 m.

m1 = 3 kgm2 = 3 kgμ = 0.3d = 1.5 mg = 9.81 m/s²
v = m/s
6.Hard
k = 3000 N/m35°μ = 0.155 kg

A spring of stiffness 3000 N/m at the bottom of a 35° slope is compressed by 15 cm against a 5 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 = 5 kgk = 3000 N/mx = 15 cmθ = 35°μ = 0.15g = 9.81 m/s²
d = m

Answer key

  1. 1. v = 24.66 m/s
  2. 2. W = 480 J
  3. 3. Wf = 76.34 J
  4. 4. P = 36.91 kW
  5. 5. v = 3.209 m/s
  6. 6. d = 0.988 m

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