State the work–energy principle.

The net work done on a particle equals its change in kinetic energy.

State the formula for gravitational potential energy.

mgh, with h the vertical height above a reference level

When is mechanical energy conserved?

When no forces other than gravity do work (no friction, resistance or driving force).

State the general energy equation when resistance acts.

Initial KE + initial GPE + work by driving forces = final KE + final GPE + work against resistances.

Does the normal reaction do work on a particle sliding along a horizontal surface?

No: it acts at right angles to the motion.

Work done and energyAQA A-Level Further Maths: Flashcards

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State the work done by a constant force $F$ moving a particle a distance $d$ in the direction of the force.

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State the work done by a constant force $F$ moving a particle a distance $d$ in the direction of the force.: $W=Fd$ , measured in joules.
What is the work done against a resistance of 30 N over 12 m?: $360$ J
State the formula for kinetic energy.: $\frac12mv^2$
State the work–energy principle.: The net work done on a particle equals its change in kinetic energy.
State the formula for gravitational potential energy.: $mgh$ , with $h$ the vertical height above a reference level
A particle slides a distance $d$ down a slope at angle $\theta$ . What GPE does it lose?: $mgd\sin\theta$
When is mechanical energy conserved?: When no forces other than gravity do work (no friction, resistance or driving force).
State the general energy equation when resistance acts.: Initial KE + initial GPE + work by driving forces = final KE + final GPE + work against resistances.
Does the normal reaction do work on a particle sliding along a horizontal surface?: No: it acts at right angles to the motion.
Find the KE of a 0.4 kg ball moving at $14\text{ m s}^{-1}$ .: $\frac12(0.4)(14^2)=39.2$ J
How do you find the friction force on a plane inclined at $\theta$ ?: $F=\mu R$ with $R=mg\cos\theta$
What is the unit of work and energy?: The joule (J), equal to 1 N m.

Exam questions on Work done and energy

A crate of mass 20 kg is pulled in a straight line across a horizontal floor by a horizontal force of 70 N. The crate moves 12 m. A constant resistance of 30 N opposes the motion.
The crate starts from rest. Find its speed after it has moved 12 m.2 marks
A ball of mass 0.4 kg is thrown vertically upwards from ground level with an initial speed of $14\text{ m s}^{-1}$ . Air resistance may be ignored. Take $g=9.8\text{ m s}^{-2}$ .
Use conservation of energy to find the speed of the ball when it is 6 m above the ground.2 marks
A skier of mass 70 kg starts from rest at the top of a straight slope inclined at $20^\circ$ to the horizontal and slides 80 m down the slope. A constant resistance of 50 N acts up the slope. Take $g=9.8\text{ m s}^{-2}$ .
Find the speed of the skier at the bottom of the slope.3 marks

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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).