1.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
Work & energy worksheet with answers
2.Easy
A 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 = 5 kgh = 20 mg = 9.81 m/s²
v = m/s
3.Medium
A block slides from rest down a slope at 15° to the horizontal. The coefficient of kinetic friction is 0.15. Find its speed v after it has slid 13 m along the slope.
θ = 15°μ = 0.15d = 13 mg = 9.81 m/s²
v = m/s
4.Medium
A toy launcher has a vertical spring of stiffness 500 N/m. A 0.15 kg ball is placed on it and the spring is compressed by 6 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 = 500 N/mx = 6 cmg = 9.81 m/s²
h = m
5.Hard
A 10 kg block is released from rest at height 4 m on a smooth ramp. At the bottom it crosses a rough horizontal strip 2 m long (μ = 0.15) and then runs onto a spring (k = 1500 N/m) on a smooth surface. Find the speed v of the block when it reaches the spring.
m = 10 kgh = 4 mL = 2 mμ = 0.15k = 1500 N/mg = 9.81 m/s²
v = m/s
6.Hard
A spring of stiffness 1000 N/m at the bottom of a 15° slope is compressed by 12 cm against a 1 kg block and released. The coefficient of kinetic friction between block and slope is 0.3. 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 = 12 cmθ = 15°μ = 0.3g = 9.81 m/s²
d = m
Answer key
- 1. v = 26.58 m/s
- 2. v = 19.81 m/s
- 3. v = 5.391 m/s
- 4. h = 0.6116 m
- 5. v = 8.52 m/s
- 6. d = 1.338 m
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