1.Easy
A 0.5 kg ball is dropped from rest from a height of 10 m. Ignore air resistance. Find its speed v just before it hits the ground.
m = 0.5 kgh = 10 mg = 9.81 m/s²
v = m/s
Work & energy worksheet with answers
2.Easy
A 5 kg block slides at 3 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 = 5 kgv = 3 m/sk = 500 N/m
x = cm
3.Medium
A 10 kg ball hangs on a light string of length 0.8 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 = 10 kgL = 0.8 mθ = 70°g = 9.81 m/s²
T = N
4.Medium
A 4 kg block slides 10 m down a slope at 40° to the horizontal, with a coefficient of kinetic friction of 0.1. Find the work Wf done against friction.
m = 4 kgθ = 40°μ = 0.1d = 10 mg = 9.81 m/s²
Wf = J
5.Hard
A spring of stiffness 5000 N/m at the bottom of a 40° slope is compressed by 8 cm against a 1 kg block and released. The coefficient of kinetic friction between block and slope is 0.15. 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 = 8 cmθ = 40°μ = 0.15g = 9.81 m/s²
d = m
6.Hard
A 2 kg block rests on a rough horizontal table (μ = 0.3). A light string runs from it over a smooth pulley at the edge of the table to a hanging 2 kg block. The system is released from rest. Find the speed v of the blocks after the hanging block has dropped 1.5 m.
m1 = 2 kgm2 = 2 kgμ = 0.3d = 1.5 mg = 9.81 m/s²
v = m/s
Answer key
- 1. v = 14.01 m/s
- 2. x = 30 cm
- 3. T = 227.2 N
- 4. Wf = 30.06 J
- 5. d = 2.153 m
- 6. v = 3.209 m/s
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