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 = 5 kggh = 43 m

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

m = 5 kgh = 43 mg = 9.81 m/s²
Ek = J
2.Easy
30°L = 1 m

A small ball hangs on a light string of length 1 m. It is pulled aside until the string makes 30° with the vertical and released from rest. Ignoring air resistance, find its speed v at the lowest point.

L = 1 mθ = 30°g = 9.81 m/s²
v = m/s
3.Medium
40°d = 4 mμ = 0.4

A block slides from rest down a slope at 40° to the horizontal. The coefficient of kinetic friction is 0.4. Find its speed v after it has slid 4 m along the slope.

θ = 40°μ = 0.4d = 4 mg = 9.81 m/s²
v = m/s
4.Medium
70°L = 1 m1 kg

A 1 kg ball hangs on a light string of length 1 m. It is pulled aside until the string makes 70° with the vertical and released from rest. Find the tension T in the string when the ball passes the lowest point.

m = 1 kgL = 1 mθ = 70°g = 9.81 m/s²
T = N
5.Hard
h = 4.5 mL = 2.5 mμ = 0.25k = 800 N/m

A 1 kg block is released from rest at height 4.5 m on a smooth ramp. At the bottom it crosses a rough horizontal strip 2.5 m long (μ = 0.25) and then runs onto a spring (k = 800 N/m) on a smooth surface. Find the maximum compression x of the spring.

m = 1 kgh = 4.5 mL = 2.5 mμ = 0.25k = 800 N/mg = 9.81 m/s²
x = cm
6.Hard
k = 3000 N/m30°μ = 0.33 kg

A spring of stiffness 3000 N/m at the bottom of a 30° slope is compressed by 10 cm against a 3 kg block and released. The coefficient of kinetic friction between block and slope is 0.3. 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 = 3000 N/mx = 10 cmθ = 30°μ = 0.3g = 9.81 m/s²
d = m

Answer key

  1. 1. Ek = 2109 J
  2. 2. v = 1.621 m/s
  3. 3. v = 5.138 m/s
  4. 4. T = 22.72 N
  5. 5. x = 30.83 cm
  6. 6. d = 0.6708 m

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