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

What these 12 flashcards ask

State the work done by a constant force at angle \theta to the displacement.
Which component of the force does work?
What work does the normal reaction do on a block sliding along a surface?
What is the sign of the work done by friction?
State the formula for power when the force is at angle \theta to the velocity.
How much potential energy does a box gain moving distance d up a slope at angle \alpha?
Find the work done by a 40 N force at 25^\circ over 30 m.
State the equation of motion for a vehicle climbing a slope with power P.
What is the greatest steady speed of a vehicle on an uphill slope?
What is the engine's work over distance s at constant speed up a slope?
What is the first thing to check when a question gives an angle?
Why must you resolve in vehicle-on-a-slope power problems?

Exam questions on Work and power with forces at an angle

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
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).