1.Easy
A crate is pulled 19 m along a level floor by a rope that makes 60° with the horizontal. The tension in the rope is 40 N. Find the work W done by the rope on the crate.
F = 40 Nd = 19 mθ = 60°
W = J
Work & energy worksheet with answers
2.Easy
A 2 kg ball is dropped from rest from a height of 36 m. Ignore air resistance. Find its speed v just before it hits the ground.
m = 2 kgh = 36 mg = 9.81 m/s²
v = m/s
3.Medium
A 1 kg block slides 14 m down a slope at 20° to the horizontal, with a coefficient of kinetic friction of 0.25. Find the work Wf done against friction.
m = 1 kgθ = 20°μ = 0.25d = 14 mg = 9.81 m/s²
Wf = J
4.Medium
A toy launcher has a vertical spring of stiffness 2000 N/m. A 0.1 kg ball is placed on it and the spring is compressed by 4 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 = 0.1 kgk = 2000 N/mx = 4 cmg = 9.81 m/s²
h = m
5.Hard
A 1 kg block is released from rest at height 3 m on a smooth ramp. At the bottom it crosses a rough horizontal strip 3.5 m long (μ = 0.2) and then runs onto a spring (k = 1000 N/m) on a smooth surface. Find the maximum compression x of the spring.
m = 1 kgh = 3 mL = 3.5 mμ = 0.2k = 1000 N/mg = 9.81 m/s²
x = cm
6.Hard
A spring of stiffness 5000 N/m at the bottom of a 20° slope is compressed by 15 cm against a 0.5 kg block and released. The coefficient of kinetic friction between block and slope is 0.25. 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 = 0.5 kgk = 5000 N/mx = 15 cmθ = 20°μ = 0.25g = 9.81 m/s²
d = m
Answer key
- 1. W = 380 J
- 2. v = 26.58 m/s
- 3. Wf = 32.26 J
- 4. h = 1.631 m
- 5. x = 21.24 cm
- 6. d = 19.88 m
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