1.Easy
A small ball hangs on a light string of length 3 m. It is pulled aside until the string makes 25° with the vertical and released from rest. Ignoring air resistance, find its speed v at the lowest point.
L = 3 mθ = 25°g = 9.81 m/s²
v = m/s
Work & energy worksheet with answers
2.Easy
A 0.5 kg ball is dropped from rest from a height of 20 m. Ignore air resistance. Find its speed v just before it hits the ground.
m = 0.5 kgh = 20 mg = 9.81 m/s²
v = m/s
3.Medium
A car travelling at 30 km/h on a level road brakes hard and skids to a stop with its wheels locked. The coefficient of kinetic friction between the tyres and the road is 0.5. Find the stopping distance d.
v = 30 km/hμ = 0.5g = 9.81 m/s²
d = m
4.Medium
A block slides from rest down a slope at 30° to the horizontal. The coefficient of kinetic friction is 0.25. Find its speed v after it has slid 4 m along the slope.
θ = 30°μ = 0.25d = 4 mg = 9.81 m/s²
v = m/s
5.Hard
A spring of stiffness 5000 N/m at the bottom of a 35° 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 = 5000 N/mx = 20 cmθ = 35°μ = 0.1g = 9.81 m/s²
d = m
6.Hard
A 2.5 kg block is released from rest at height 5 m on a smooth ramp. At the bottom it crosses a rough horizontal strip 2.5 m long (μ = 0.2) and then runs onto a spring (k = 5000 N/m) on a smooth surface. Find the speed v of the block when it reaches the spring.
m = 2.5 kgh = 5 mL = 2.5 mμ = 0.2k = 5000 N/mg = 9.81 m/s²
v = m/s
Answer key
- 1. v = 2.348 m/s
- 2. v = 19.81 m/s
- 3. d = 7.079 m
- 4. v = 4.717 m/s
- 5. d = 3.11 m
- 6. v = 9.396 m/s
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