Work and power with forces at an angleAQA A-Level Further Maths: Mind map

Exam questions on Work and power with forces at an angle

1. A child pulls a sledge of mass 15 kg in a straight line along horizontal ground by a rope inclined at $25^\circ$ above the horizontal. The tension in the rope is 40 N and the sledge moves 30 m. A constant horizontal resistance of 28 N acts on the sledge. The sledge starts from rest.
   Find the power developed by the rope at the instant when the sledge is moving at $5\text{ m s}^{-1}$.2 marks
2. A car of mass 1000 kg travels up a straight road inclined at an angle $\theta$ to the horizontal, where $\sin\theta=0.1$. The resistance to motion is a constant 400 N and the engine works at a constant 25 kW. Take $g=9.8\text{ m s}^{-2}$.
   Find the power the engine must develop for the car to climb at a constant $15\text{ m s}^{-1}$.2 marks
3. A box of mass 20 kg is pulled from rest up a line of greatest slope of a smooth ramp inclined at $20^\circ$ to the horizontal. The pulling force is a constant 120 N, applied by a rope that makes an angle of $30^\circ$ with the ramp, above it. The box moves 6 m up the ramp. Take $g=9.8\text{ m s}^{-2}$.
   Find the work done by the rope and the gain in gravitational potential energy of the box.3 marks