Work & energy worksheet with answers

A small ball hangs on a light string of length 2 m. It is pulled aside until the string makes 90° with the vertical and released from rest. Ignoring air resistance, find its speed v at the lowest point.

A crate is pulled 13 m along a level floor by a rope that makes 40° with the horizontal. The tension in the rope is 200 N. Find the work W done by the rope on the crate.

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 2 m along the slope.

A toy launcher has a vertical spring of stiffness 1000 N/m. A 0.2 kg ball is placed on it and the spring is compressed by 6 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.

A 2 kg cart is released from rest at a height of 7.8 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.

A 1 kg block is released from rest at height 1 m on a smooth ramp. At the bottom it crosses a rough horizontal strip 1 m long (μ = 0.1) and then runs onto a spring (k = 1500 N/m) on a smooth surface. Find the maximum compression x of the spring.