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
100 kgh = 14 mt = 5 s

A hoist lifts a 100 kg load at constant speed through a height of 14 m in 5 s. Find the average power P it delivers to the load, in kW.

m = 100 kgh = 14 mt = 5 sg = 9.81 m/s²
P = kW
2.Easy
m = 4 kggh = 32 m

A 4 kg ball is dropped from rest from a height of 32 m. Ignore air resistance. Find its kinetic energy Ek just before it hits the ground.

m = 4 kgh = 32 mg = 9.81 m/s²
Ek = J
3.Medium
20°L = 0.8 m10 kg

A 10 kg ball hangs on a light string of length 0.8 m. It is pulled aside until the string makes 20° with the vertical and released from rest. Find the tension T in the string when the ball passes the lowest point.

m = 10 kgL = 0.8 mθ = 20°g = 9.81 m/s²
T = N
4.Medium
90 km/h6°1000 kg

A 1000 kg car drives up a 6° slope at a constant 90 km/h. Air resistance and rolling resistance together amount to 550 N. Find the power P the wheels must deliver, in kW.

m = 1000 kgθ = 6°Fr = 550 Nv = 90 km/hg = 9.81 m/s²
P = kW
5.Hard
h = 4.5 mL = 5 mμ = 0.2k = 2500 N/m

A 0.5 kg block is released from rest at height 4.5 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 = 0.5 kgh = 4.5 mL = 5 mμ = 0.2k = 2500 N/mg = 9.81 m/s²
x = cm
6.Hard
k = 800 N/m25°μ = 0.15 kg

A spring of stiffness 800 N/m at the bottom of a 25° slope is compressed by 20 cm against a 5 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 = 5 kgk = 800 N/mx = 20 cmθ = 25°μ = 0.1g = 9.81 m/s²
d = m

Answer key

  1. 1. P = 2.747 kW
  2. 2. Ek = 1256 J
  3. 3. T = 109.9 N
  4. 4. P = 39.39 kW
  5. 5. x = 11.72 cm
  6. 6. d = 0.6356 m

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