1.Easy
A small ball hangs on a light string of length 3 m. It is pulled aside until the string makes 35° with the vertical and released from rest. Ignoring air resistance, find its speed v at the lowest point.
L = 3 mθ = 35°g = 9.81 m/s²
v = m/s
Work & energy worksheet with answers
2.Easy
A 2.5 kg ball is dropped from rest from a height of 50 m. Ignore air resistance. Find its kinetic energy Ek just before it hits the ground.
m = 2.5 kgh = 50 mg = 9.81 m/s²
Ek = J
3.Medium
A block slides from rest down a slope at 45° to the horizontal. The coefficient of kinetic friction is 0.4. Find its speed v after it has slid 6 m along the slope.
θ = 45°μ = 0.4d = 6 mg = 9.81 m/s²
v = m/s
4.Medium
A toy launcher has a vertical spring of stiffness 2000 N/m. A 0.5 kg ball is placed on it and the spring is compressed by 8 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 = 0.5 kgk = 2000 N/mx = 8 cmg = 9.81 m/s²
h = m
5.Hard
A 1 kg block is released from rest at height 2 m on a smooth ramp. At the bottom it crosses a rough horizontal strip 3.5 m long (μ = 0.1) and then runs onto a spring (k = 5000 N/m) on a smooth surface. Find the maximum compression x of the spring.
m = 1 kgh = 2 mL = 3.5 mμ = 0.1k = 5000 N/mg = 9.81 m/s²
x = cm
6.Hard
A 2 kg block is released from rest at height 2 m on a smooth ramp. At the bottom it crosses a rough horizontal strip 1 m long (μ = 0.25) and then runs onto a spring (k = 2000 N/m) on a smooth surface. Find the speed v of the block when it reaches the spring.
m = 2 kgh = 2 mL = 1 mμ = 0.25k = 2000 N/mg = 9.81 m/s²
v = m/s
Answer key
- 1. v = 3.263 m/s
- 2. Ek = 1226 J
- 3. v = 7.067 m/s
- 4. h = 1.305 m
- 5. x = 8.046 cm
- 6. v = 5.86 m/s
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