1.Easy
A 4 kg block slides at 2 m/s on a smooth horizontal surface into a spring of stiffness 400 N/m. Find the maximum compression x of the spring, in cm.
m = 4 kgv = 2 m/sk = 400 N/m
x = cm
Work & energy worksheet with answers
2.Easy
A 1 kg ball is dropped from rest from a height of 24 m. Ignore air resistance. Find its speed v just before it hits the ground.
m = 1 kgh = 24 mg = 9.81 m/s²
v = m/s
3.Medium
A toy launcher has a vertical spring of stiffness 500 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 = 500 N/mx = 8 cmg = 9.81 m/s²
h = m
4.Medium
A block slides from rest down a slope at 30° to the horizontal. The coefficient of kinetic friction is 0.4. Find its speed v after it has slid 15 m along the slope.
θ = 30°μ = 0.4d = 15 mg = 9.81 m/s²
v = m/s
5.Hard
A 1 kg cart is released from rest at a height of 18 m on a smooth track that leads into a vertical circular loop of radius 4 m. Find the normal force N the track exerts on the cart at the top of the loop.
m = 1 kgh = 18 mR = 4 mg = 9.81 m/s²
N = N
6.Hard
A 4 kg block rests on a rough horizontal table (μ = 0.2). A light string runs from it over a smooth pulley at the edge of the table to a hanging 3 kg block. The system is released from rest. Find the speed v of the blocks after the hanging block has dropped 2 m.
m1 = 4 kgm2 = 3 kgμ = 0.2d = 2 mg = 9.81 m/s²
v = m/s
Answer key
- 1. x = 20 cm
- 2. v = 21.7 m/s
- 3. h = 0.3262 m
- 4. v = 6.723 m/s
- 5. N = 39.24 N
- 6. v = 3.512 m/s
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