1.Easy
A 1 kg block slides at 5.5 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 = 1 kgv = 5.5 m/sk = 1000 N/m
x = cm
Work & energy worksheet with answers
2.Easy
A 5 kg ball is dropped from rest from a height of 22 m. Ignore air resistance. Find its kinetic energy Ek just before it hits the ground.
m = 5 kgh = 22 mg = 9.81 m/s²
Ek = J
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 4 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 = 4 cmg = 9.81 m/s²
h = m
4.Medium
A 1000 kg car drives up a 5° slope at a constant 54 km/h. Air resistance and rolling resistance together amount to 450 N. Find the power P the wheels must deliver, in kW.
m = 1000 kgθ = 5°Fr = 450 Nv = 54 km/hg = 9.81 m/s²
P = kW
5.Hard
A 5 kg block is released from rest at height 1 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 = 500 N/m) on a smooth surface. Find the maximum compression x of the spring.
m = 5 kgh = 1 mL = 2 mμ = 0.15k = 500 N/mg = 9.81 m/s²
x = cm
6.Hard
A 0.5 kg cart is released from rest at a height of 9 m on a smooth track that leads into a vertical circular loop of radius 3 m. Find the speed v of the cart at the top of the loop.
m = 0.5 kgh = 9 mR = 3 mg = 9.81 m/s²
v = m/s
Answer key
- 1. x = 17.39 cm
- 2. Ek = 1079 J
- 3. h = 0.8155 m
- 4. P = 19.57 kW
- 5. x = 37.06 cm
- 6. v = 7.672 m/s
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