1.Easy
A 0.5 kg block slides at 3 m/s on a smooth horizontal surface into a spring of stiffness 2000 N/m. Find the maximum compression x of the spring, in cm.
m = 0.5 kgv = 3 m/sk = 2000 N/m
x = cm
Work & energy worksheet with answers
2.Easy
A small ball hangs on a light string of length 1.2 m. It is pulled aside until the string makes 30° with the vertical and released from rest. Ignoring air resistance, find its speed v at the lowest point.
L = 1.2 mθ = 30°g = 9.81 m/s²
v = m/s
3.Medium
A 1800 kg car drives up a 4° slope at a constant 36 km/h. Air resistance and rolling resistance together amount to 300 N. Find the power P the wheels must deliver, in kW.
m = 1800 kgθ = 4°Fr = 300 Nv = 36 km/hg = 9.81 m/s²
P = kW
4.Medium
A block slides from rest down a slope at 45° to the horizontal. The coefficient of kinetic friction is 0.2. Find its speed v after it has slid 9 m along the slope.
θ = 45°μ = 0.2d = 9 mg = 9.81 m/s²
v = m/s
5.Hard
A 5 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 = 0.15) and then runs onto a spring (k = 5000 N/m) on a smooth surface. Find the maximum compression x of the spring.
m = 5 kgh = 2 mL = 3.5 mμ = 0.15k = 5000 N/mg = 9.81 m/s²
x = cm
6.Hard
A 5 kg cart is released from rest at a height of 2.8 m on a smooth track that leads into a vertical circular loop of radius 1 m. Find the normal force N the track exerts on the cart at the top of the loop.
m = 5 kgh = 2.8 mR = 1 mg = 9.81 m/s²
N = N
Answer key
- 1. x = 4.743 cm
- 2. v = 1.776 m/s
- 3. P = 15.32 kW
- 4. v = 9.994 m/s
- 5. x = 17.01 cm
- 6. N = 29.43 N
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