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 = 10 kggh = 38 m

A 10 kg ball is dropped from rest from a height of 38 m. Ignore air resistance. Find its speed v just before it hits the ground.

m = 10 kgh = 38 mg = 9.81 m/s²
v = m/s
2.Easy
m = 5 kggh = 2 m

A 5 kg ball is dropped from rest from a height of 2 m. Ignore air resistance. Find its speed v just before it hits the ground.

m = 5 kgh = 2 mg = 9.81 m/s²
v = m/s
3.Medium
30°d = 8 mμ = 0.3

A block slides from rest down a slope at 30° to the horizontal. The coefficient of kinetic friction is 0.3. Find its speed v after it has slid 8 m along the slope.

θ = 30°μ = 0.3d = 8 mg = 9.81 m/s²
v = m/s
4.Medium
0.1 kgk = 1000 N/mh = ?

A toy launcher has a vertical spring of stiffness 1000 N/m. A 0.1 kg ball is placed on it and the spring is compressed by 8 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 = 1000 N/mx = 8 cmg = 9.81 m/s²
h = m
5.Hard
3 kg2 kgμ = 0.15d = 2 m

A 3 kg block rests on a rough horizontal table (μ = 0.15). A light string runs from it over a smooth pulley at the edge of the table to a hanging 2 kg block. The system is released from rest. Find the speed v of the blocks after the hanging block has dropped 2 m.

m1 = 3 kgm2 = 2 kgμ = 0.15d = 2 mg = 9.81 m/s²
v = m/s
6.Hard
k = 5000 N/m30°μ = 0.153 kg

A spring of stiffness 5000 N/m at the bottom of a 30° slope is compressed by 15 cm against a 3 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 = 3 kgk = 5000 N/mx = 15 cmθ = 30°μ = 0.15g = 9.81 m/s²
d = m

Answer key

  1. 1. v = 27.3 m/s
  2. 2. v = 6.264 m/s
  3. 3. v = 6.14 m/s
  4. 4. h = 3.262 m
  5. 5. v = 3.488 m/s
  6. 6. d = 3.034 m

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