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
0.5 kgv = 6 m/sk = 1000 N/m

A 0.5 kg block slides at 6 m/s on a smooth horizontal surface into a spring of stiffness 1000 N/m. Find the maximum compression x of the spring, in cm.

m = 0.5 kgv = 6 m/sk = 1000 N/m
x = cm
2.Easy
m = 0.5 kggh = 18 m

A 0.5 kg ball is dropped from rest from a height of 18 m. Ignore air resistance. Find its kinetic energy Ek just before it hits the ground.

m = 0.5 kgh = 18 mg = 9.81 m/s²
Ek = J
3.Medium
0.2 kgk = 400 N/mh = ?

A toy launcher has a vertical spring of stiffness 400 N/m. A 0.2 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 = 0.2 kgk = 400 N/mx = 10 cmg = 9.81 m/s²
h = m
4.Medium
35°d = 8 mμ = 0.3

A 2.5 kg block slides 8 m down a slope at 35° to the horizontal, with a coefficient of kinetic friction of 0.3. Find the work Wf done against friction.

m = 2.5 kgθ = 35°μ = 0.3d = 8 mg = 9.81 m/s²
Wf = J
5.Hard
4 kg2 kgμ = 0.1d = 0.5 m

A 4 kg block rests on a rough horizontal table (μ = 0.1). 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 0.5 m.

m1 = 4 kgm2 = 2 kgμ = 0.1d = 0.5 mg = 9.81 m/s²
v = m/s
6.Hard
h = 5 mL = 1.5 mμ = 0.3k = 500 N/m

A 4 kg block is released from rest at height 5 m on a smooth ramp. At the bottom it crosses a rough horizontal strip 1.5 m long (μ = 0.3) and then runs onto a spring (k = 500 N/m) on a smooth surface. Find the maximum compression x of the spring.

m = 4 kgh = 5 mL = 1.5 mμ = 0.3k = 500 N/mg = 9.81 m/s²
x = cm

Answer key

  1. 1. x = 13.42 cm
  2. 2. Ek = 88.29 J
  3. 3. h = 1.019 m
  4. 4. Wf = 48.22 J
  5. 5. v = 1.617 m/s
  6. 6. x = 84.51 cm

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