1.Easy
A hoist lifts an 80 kg load at constant speed through a height of 4 m in 30 s. Find the average power P it delivers to the load, in W.
m = 80 kgh = 4 mt = 30 sg = 9.81 m/s²
P = W
Work & energy worksheet with answers
2.Easy
A 5 kg block slides at 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 = 5 kgv = 5 m/sk = 1000 N/m
x = cm
3.Medium
A toy launcher has a vertical spring of stiffness 1000 N/m. A 0.1 kg ball is placed on it and the spring is compressed by 3 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 = 0.1 kgk = 1000 N/mx = 3 cmg = 9.81 m/s²
h = m
4.Medium
A block slides from rest down a slope at 35° to the horizontal. The coefficient of kinetic friction is 0.25. Find its speed v after it has slid 7 m along the slope.
θ = 35°μ = 0.25d = 7 mg = 9.81 m/s²
v = m/s
5.Hard
A 5 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 = 0.2) and then runs onto a spring (k = 4000 N/m) on a smooth surface. Find the speed v of the block when it reaches the spring.
m = 5 kgh = 4 mL = 2 mμ = 0.2k = 4000 N/mg = 9.81 m/s²
v = m/s
6.Hard
A 1 kg cart is released from rest at a height of 6.8 m on a smooth track that leads into a vertical circular loop of radius 1.5 m. Find the speed v of the cart at the top of the loop.
m = 1 kgh = 6.8 mR = 1.5 mg = 9.81 m/s²
v = m/s
Answer key
- 1. P = 104.6 W
- 2. x = 35.36 cm
- 3. h = 0.4587 m
- 4. v = 7.117 m/s
- 5. v = 8.404 m/s
- 6. v = 8.635 m/s
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