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
2 kgv = 4 m/sk = 500 N/m

A 2 kg block slides at 4 m/s on a smooth horizontal surface into a spring of stiffness 500 N/m. Find the maximum compression x of the spring, in cm.

m = 2 kgv = 4 m/sk = 500 N/m
x = cm
2.Easy
1 kgv = 3.5 m/sk = 1000 N/m

A 1 kg block slides at 3.5 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 = 1 kgv = 3.5 m/sk = 1000 N/m
x = cm
3.Medium
50°L = 0.8 m2 kg

A 2 kg ball hangs on a light string of length 0.8 m. It is pulled aside until the string makes 50° with the vertical and released from rest. Find the tension T in the string when the ball passes the lowest point.

m = 2 kgL = 0.8 mθ = 50°g = 9.81 m/s²
T = N
4.Medium
30°d = 10 mμ = 0.15

A 10 kg block slides 10 m down a slope at 30° to the horizontal, with a coefficient of kinetic friction of 0.15. Find the work Wf done against friction.

m = 10 kgθ = 30°μ = 0.15d = 10 mg = 9.81 m/s²
Wf = J
5.Hard
k = 5000 N/m35°μ = 0.11 kg

A spring of stiffness 5000 N/m at the bottom of a 35° slope is compressed by 10 cm against a 1 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 = 1 kgk = 5000 N/mx = 10 cmθ = 35°μ = 0.1g = 9.81 m/s²
d = m
6.Hard
h = 3 mL = 5 mμ = 0.2k = 2500 N/m

A 10 kg block is released from rest at height 3 m on a smooth ramp. At the bottom it crosses a rough horizontal strip 5 m long (μ = 0.2) and then runs onto a spring (k = 2500 N/m) on a smooth surface. Find the maximum compression x of the spring.

m = 10 kgh = 3 mL = 5 mμ = 0.2k = 2500 N/mg = 9.81 m/s²
x = cm

Answer key

  1. 1. x = 25.3 cm
  2. 2. x = 11.07 cm
  3. 3. T = 33.64 N
  4. 4. Wf = 127.4 J
  5. 5. d = 3.888 m
  6. 6. x = 39.62 cm

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