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 = 46 m

A 1 kg ball is dropped from rest from a height of 46 m. Ignore air resistance. Find its kinetic energy Ek just before it hits the ground.

m = 1 kgh = 46 mg = 9.81 m/s²
Ek = J
2.Easy
m = 0.5 kggh = 37 m

A 0.5 kg ball is dropped from rest from a height of 37 m. Ignore air resistance. Find its kinetic energy Ek just before it hits the ground.

m = 0.5 kgh = 37 mg = 9.81 m/s²
Ek = J
3.Medium
54 km/h6°1200 kg

A 1200 kg car drives up a 6° slope at a constant 54 km/h. Air resistance and rolling resistance together amount to 550 N. Find the power P the wheels must deliver, in kW.

m = 1200 kgθ = 6°Fr = 550 Nv = 54 km/hg = 9.81 m/s²
P = kW
4.Medium
0.15 kgk = 400 N/mh = ?

A toy launcher has a vertical spring of stiffness 400 N/m. A 0.15 kg ball is placed on it and the spring is compressed by 8 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 = 0.15 kgk = 400 N/mx = 8 cmg = 9.81 m/s²
h = m
5.Hard
k = 5000 N/m25°μ = 0.15 kg

A spring of stiffness 5000 N/m at the bottom of a 25° slope is compressed by 12 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 = 5000 N/mx = 12 cmθ = 25°μ = 0.1g = 9.81 m/s²
d = m
6.Hard
h = 1 mL = 2.5 mμ = 0.25k = 2000 N/m

A 10 kg block is released from rest at height 1 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 = 2000 N/m) on a smooth surface. Find the speed v of the block when it reaches the spring.

m = 10 kgh = 1 mL = 2.5 mμ = 0.25k = 2000 N/mg = 9.81 m/s²
v = m/s

Answer key

  1. 1. Ek = 451.3 J
  2. 2. Ek = 181.5 J
  3. 3. P = 26.71 kW
  4. 4. h = 0.8699 m
  5. 5. d = 1.43 m
  6. 6. v = 2.712 m/s

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