1.Easy
A 4 kg block slides at 1.5 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 = 4 kgv = 1.5 m/sk = 1000 N/m
x = cm
Work & energy worksheet with answers
2.Easy
A 4 kg ball is dropped from rest from a height of 7 m. Ignore air resistance. Find its kinetic energy Ek just before it hits the ground.
m = 4 kgh = 7 mg = 9.81 m/s²
Ek = J
3.Medium
A block slides from rest down a slope at 35° to the horizontal. The coefficient of kinetic friction is 0.3. Find its speed v after it has slid 12 m along the slope.
θ = 35°μ = 0.3d = 12 mg = 9.81 m/s²
v = m/s
4.Medium
A 1 kg ball hangs on a light string of length 1 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 = 1 kgL = 1 mθ = 20°g = 9.81 m/s²
T = N
5.Hard
A spring of stiffness 1000 N/m at the bottom of a 25° slope is compressed by 8 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 = 1000 N/mx = 8 cmθ = 25°μ = 0.1g = 9.81 m/s²
d = m
6.Hard
A 5 kg block starts from rest at the bottom of a 25° slope and is pulled up the slope by a constant force of 40 N parallel to the slope. The coefficient of kinetic friction is 0.1. Find the speed v of the block after it has moved 10 m up the slope.
m = 5 kgF = 40 Nθ = 25°μ = 0.1d = 10 mg = 9.81 m/s²
v = m/s
Answer key
- 1. x = 9.487 cm
- 2. Ek = 274.7 J
- 3. v = 8.785 m/s
- 4. T = 10.99 N
- 5. d = 0.6356 m
- 6. v = 7.701 m/s
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