1.Easy
A crate is pulled 14 m along a level floor by a rope that makes 35° with the horizontal. The tension in the rope is 110 N. Find the work W done by the rope on the crate.
F = 110 Nd = 14 mθ = 35°
W = J
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 40° with the vertical and released from rest. Ignoring air resistance, find its speed v at the lowest point.
L = 0.8 mθ = 40°g = 9.81 m/s²
v = m/s
3.Medium
An 800 kg car drives up an 8° slope at a constant 90 km/h. Air resistance and rolling resistance together amount to 550 N. Find the power P the wheels must deliver, in kW.
m = 800 kgθ = 8°Fr = 550 Nv = 90 km/hg = 9.81 m/s²
P = kW
4.Medium
A block slides from rest down a slope at 40° to the horizontal. The coefficient of kinetic friction is 0.2. Find its speed v after it has slid 8 m along the slope.
θ = 40°μ = 0.2d = 8 mg = 9.81 m/s²
v = m/s
5.Hard
A 2 kg block is released from rest at height 2 m on a smooth ramp. At the bottom it crosses a rough horizontal strip 4 m long (μ = 0.3) and then runs onto a spring (k = 800 N/m) on a smooth surface. Find the maximum compression x of the spring.
m = 2 kgh = 2 mL = 4 mμ = 0.3k = 800 N/mg = 9.81 m/s²
x = cm
6.Hard
A 2.5 kg block is released from rest at height 2 m on a smooth ramp. At the bottom it crosses a rough horizontal strip 4.5 m long (μ = 0.15) 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 = 2.5 kgh = 2 mL = 4.5 mμ = 0.15k = 2000 N/mg = 9.81 m/s²
v = m/s
Answer key
- 1. W = 1261 J
- 2. v = 1.916 m/s
- 3. P = 41.06 kW
- 4. v = 8.766 m/s
- 5. x = 19.81 cm
- 6. v = 5.099 m/s
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