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 = 1 kggh = 45 m

A 1 kg ball is dropped from rest from a height of 45 m. Ignore air resistance. Find its kinetic energy Ek just before it hits the ground.

m = 1 kgh = 45 mg = 9.81 m/s²
Ek = J
2.Easy
m = 5 kggh = 43 m

A 5 kg ball is dropped from rest from a height of 43 m. Ignore air resistance. Find its speed v just before it hits the ground.

m = 5 kgh = 43 mg = 9.81 m/s²
v = m/s
3.Medium
35°d = 10 mμ = 0.3

A 0.5 kg block slides 10 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 = 0.5 kgθ = 35°μ = 0.3d = 10 mg = 9.81 m/s²
Wf = J
4.Medium
15°d = 19 mμ = 0.15

A block slides from rest down a slope at 15° to the horizontal. The coefficient of kinetic friction is 0.15. Find its speed v after it has slid 19 m along the slope.

θ = 15°μ = 0.15d = 19 mg = 9.81 m/s²
v = m/s
5.Hard
h = 10.5 mR = 3 mN = ?

A 10 kg cart is released from rest at a height of 10.5 m on a smooth track that leads into a vertical circular loop of radius 3 m. Find the normal force N the track exerts on the cart at the top of the loop.

m = 10 kgh = 10.5 mR = 3 mg = 9.81 m/s²
N = N
6.Hard
k = 5000 N/m35°μ = 0.13 kg

A spring of stiffness 5000 N/m at the bottom of a 35° slope is compressed by 20 cm against a 3 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 = 3 kgk = 5000 N/mx = 20 cmθ = 35°μ = 0.1g = 9.81 m/s²
d = m

Answer key

  1. 1. Ek = 441.5 J
  2. 2. v = 29.05 m/s
  3. 3. Wf = 12.05 J
  4. 4. v = 6.517 m/s
  5. 5. N = 196.2 N
  6. 6. d = 5.184 m

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