State the work-energy principle.

Work done on a particle equals its change in kinetic energy.

When is mechanical energy conserved?

When no forces other than gravity (or other conservative forces) do work.

P=\frac{work done}{time}, in watts.

Condition at the maximum speed of a vehicle?

Acceleration is zero, so driving force equals total resistance.

Equation of motion for a car on a slope?

\frac{P}{v}-R-mg\sin\theta=ma going up the slope.

Work, energy and powerEdexcel A-Level Further Maths: Flashcards

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Work done by a constant force $F$ over distance $d$?

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Work done by a constant force $F$ over distance $d$ ?: $Fd$ , or $Fd\cos\theta$ if the force is at angle $\theta$ to the motion.
Kinetic energy?: $\frac12mv^2$
Gravitational potential energy?: $mgh$
State the work-energy principle.: Work done on a particle equals its change in kinetic energy.
When is mechanical energy conserved?: When no forces other than gravity (or other conservative forces) do work.
Friction when a particle is moving?: $F=\mu R$
Normal reaction on a slope at angle $\alpha$ (no other vertical forces)?: $R=mg\cos\alpha$
Power in terms of force and speed?: $P=Fv$
Power as a rate?: $P=\frac{\text{work done}}{\text{time}}$ , in watts.
Condition at the maximum speed of a vehicle?: Acceleration is zero, so driving force equals total resistance.
Equation of motion for a car on a slope?: $\frac{P}{v}-R-mg\sin\theta=ma$ going up the slope.
What is $24$ kW in watts?: $24\,000$ W

Exam questions on Work, energy and power

A stone of mass $0.2$ kg is thrown vertically upwards from ground level with speed $15$ m s $^{-1}$ . Air resistance may be ignored. Take $g=9.8$ m s $^{-2}$ .
Find the speed of the stone when it is $5$ m above the ground, on the way up.2 marks
A car of mass $1200$ kg has its engine working at a constant power of $24$ kW. The resistance to the car's motion is constant at $600$ N on every road.
The car climbs a straight road inclined at an angle $\alpha$ to the horizontal, where $\sin\alpha=\frac{1}{20}$ , at a constant speed. Find this speed.2 marks
A particle of mass $4$ kg is projected up a line of greatest slope of a rough plane that is inclined at $30^\circ$ to the horizontal, with initial speed $8$ m s $^{-1}$ . The coefficient of friction between the particle and the plane is $0.3$ . Take $g=9.8$ m s $^{-2}$ .
Find the magnitude of the frictional force acting on the particle.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).