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 = 0.5 kggh = 12 m

A 0.5 kg ball is dropped from rest from a height of 12 m. Ignore air resistance. Find its kinetic energy Ek just before it hits the ground.

m = 0.5 kgh = 12 mg = 9.81 m/s²
Ek = J
2.Easy
m = 2.5 kggh = 18 m

A 2.5 kg ball is dropped from rest from a height of 18 m. Ignore air resistance. Find its speed v just before it hits the ground.

m = 2.5 kgh = 18 mg = 9.81 m/s²
v = m/s
3.Medium
25°d = 3 mμ = 0.2

A block slides from rest down a slope at 25° to the horizontal. The coefficient of kinetic friction is 0.2. Find its speed v after it has slid 3 m along the slope.

θ = 25°μ = 0.2d = 3 mg = 9.81 m/s²
v = m/s
4.Medium
45°d = 5 mμ = 0.35

A 2.5 kg block slides 5 m down a slope at 45° to the horizontal, with a coefficient of kinetic friction of 0.35. Find the work Wf done against friction.

m = 2.5 kgθ = 45°μ = 0.35d = 5 mg = 9.81 m/s²
Wf = J
5.Hard
h = 2 mL = 4.5 mμ = 0.1k = 1500 N/m

A 0.5 kg block is released from rest at height 2 m on a smooth ramp. At the bottom it crosses a rough horizontal strip 4.5 m long (μ = 0.1) and then runs onto a spring (k = 1500 N/m) on a smooth surface. Find the speed v of the block when it reaches the spring.

m = 0.5 kgh = 2 mL = 4.5 mμ = 0.1k = 1500 N/mg = 9.81 m/s²
v = m/s
6.Hard
k = 800 N/m15°μ = 0.15 kg

A spring of stiffness 800 N/m at the bottom of a 15° slope is compressed by 20 cm against a 5 kg block and released. The coefficient of kinetic friction between block and slope is 0.1. 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 = 800 N/mx = 20 cmθ = 15°μ = 0.1g = 9.81 m/s²
d = m

Answer key

  1. 1. Ek = 58.86 J
  2. 2. v = 18.79 m/s
  3. 3. v = 3.769 m/s
  4. 4. Wf = 30.35 J
  5. 5. v = 5.515 m/s
  6. 6. d = 0.9178 m

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