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
1 kgv = 6 m/sk = 800 N/m

A 1 kg block slides at 6 m/s on a smooth horizontal surface into a spring of stiffness 800 N/m. Find the maximum compression x of the spring, in cm.

m = 1 kgv = 6 m/sk = 800 N/m
x = cm
2.Easy
45°L = 1.5 m

A small ball hangs on a light string of length 1.5 m. It is pulled aside until the string makes 45° with the vertical and released from rest. Ignoring air resistance, find its speed v at the lowest point.

L = 1.5 mθ = 45°g = 9.81 m/s²
v = m/s
3.Medium
45°d = 14 mμ = 0.2

A block slides from rest down a slope at 45° to the horizontal. The coefficient of kinetic friction is 0.2. Find its speed v after it has slid 14 m along the slope.

θ = 45°μ = 0.2d = 14 mg = 9.81 m/s²
v = m/s
4.Medium
20°d = 5 mμ = 0.15

A 10 kg block slides 5 m down a slope at 20° to the horizontal, with a coefficient of kinetic friction of 0.15. Find the work Wf done against friction.

m = 10 kgθ = 20°μ = 0.15d = 5 mg = 9.81 m/s²
Wf = J
5.Hard
h = 3 mL = 2 mμ = 0.3k = 4000 N/m

A 4 kg block is released from rest at height 3 m on a smooth ramp. At the bottom it crosses a rough horizontal strip 2 m long (μ = 0.3) and then runs onto a spring (k = 4000 N/m) on a smooth surface. Find the speed v of the block when it reaches the spring.

m = 4 kgh = 3 mL = 2 mμ = 0.3k = 4000 N/mg = 9.81 m/s²
v = m/s
6.Hard
5 kg2 kgμ = 0.3d = 2.5 m

A 5 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 2 kg block. The system is released from rest. Find the speed v of the blocks after the hanging block has dropped 2.5 m.

m1 = 5 kgm2 = 2 kgμ = 0.3d = 2.5 mg = 9.81 m/s²
v = m/s

Answer key

  1. 1. x = 21.21 cm
  2. 2. v = 2.936 m/s
  3. 3. v = 12.47 m/s
  4. 4. Wf = 69.14 J
  5. 5. v = 6.862 m/s
  6. 6. v = 1.872 m/s

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