1.Easy
A 2.5 kg block slides at 1.5 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 = 2.5 kgv = 1.5 m/sk = 500 N/m
x = cm
Work & energy worksheet with answers
2.Easy
A small ball hangs on a light string of length 0.8 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 = 0.8 mθ = 35°g = 9.81 m/s²
v = m/s
3.Medium
A 1 kg ball hangs on a light string of length 1 m. It is pulled aside until the string makes 60° 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 = 60°g = 9.81 m/s²
T = N
4.Medium
A toy launcher has a vertical spring of stiffness 1500 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 = 1500 N/mx = 6 cmg = 9.81 m/s²
h = m
5.Hard
A 4 kg block is released from rest at height 2 m on a smooth ramp. At the bottom it crosses a rough horizontal strip 5 m long (μ = 0.2) 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 = 4 kgh = 2 mL = 5 mμ = 0.2k = 2000 N/mg = 9.81 m/s²
v = m/s
6.Hard
A 2.5 kg block is released from rest at height 3.5 m on a smooth ramp. At the bottom it crosses a rough horizontal strip 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 = 3.5 mL = 5 mμ = 0.2k = 5000 N/mg = 9.81 m/s²
v = m/s
Answer key
- 1. x = 10.61 cm
- 2. v = 1.685 m/s
- 3. T = 19.62 N
- 4. h = 1.835 m
- 5. v = 4.429 m/s
- 6. v = 7.004 m/s
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