Edexcel A-Level Mathematics A2 M2.3 Work and Energy Questions

Practise M2 work and energy by linking kinetic energy, gravitational potential energy, resistance, friction and power in particle or vehicle models.

Exam points

Build a work-energy equation with KE change, GPE change and work against friction or resistance.
Use P=Fv or conservation of mechanical energy to find speed, acceleration or total work done.

Covered syllabus points

M2.3.1 - Kinetic and potential energy, work

[Maximum number: 9]

A cyclist is travelling on a straight horizontal road and working at a constant rate of 500 W .

The total mass of the cyclist and her cycle is 80 kg .
The total resistance to the motion of the cyclist is modelled as a constant force of magnitude 60 N .

(a)

Using this model, find the total work done by the cyclist in the journey from A to B.

Later on, the cyclist is travelling up a straight road which is inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha=\frac{1}{20}$

The cyclist is now working at a constant rate of P watts and has a constant speed of $7 \mathrm{~m} \mathrm{~s}^{-1}$

The total resistance to the motion of the cyclist from non-gravitational forces is again modelled as a constant force of magnitude 60 N.

[ 5 ]

$\text{Gain in KE}=\frac12\times80\times8^2=2560\ \mathrm J$ $\text{Gain in GPE}=80\times9.8\times300=235200\ \mathrm J$ $\text{Work against resistance}=20000\times60$ $\text{Total work}=40\times64+80\times9.8\times300+20000\times60=1437760\ \mathrm J$ $1440\ \mathrm{kJ}\quad\text{or}\quad 1400\ \mathrm{kJ}$

(b)

Using this model, find the value of P

[ 4 ]

Equation of motion
$\begin{aligned} F-60-80g\sin\alpha&=0\\ \frac{P}{7}-60-80g\left(\frac1{20}\right)&=0 \end{aligned}$ $P=694\ \text{W}\quad\text{or}\quad 690\ \text{W}$

[Maximum number: 8]

A rough plane is inclined to the horizontal at an angle $\alpha$ , where $\tan \alpha=\frac{3}{4}$

A particle P of mass m is held at rest at a point A on the plane.
The particle is then projected with speed u up a line of greatest slope of the plane and comes to instantaneous rest at the point B.

The coefficient of friction between the particle and the plane is $\frac{1}{7}$

(a)

Given that $u=\sqrt{10ag}$ , use the work-energy principle to find AB in terms of a.

[ 4 ]

Energy equation: PE gain plus work done against friction equals KE lost, or equivalent.
The question tells candidates to use work-energy. Need all terms and dimensionally correct;
condone sign errors and sine/cosine confusion.
$\frac{4mgd}{35}+mgd\sin\alpha=\frac12m\times10ag$
or
$\frac{4mgd}{35}+mgd\times\frac35=\frac12m\times10ag$
Unsimplified equation with at most one error;
correct unsimplified equation.
d=AB=7a
cao

(b)

to find, in terms of a and g, the speed of P when it returns to A.

[ 4 ]

Energy equation.
Need all terms and dimensionally correct;
condone sign errors.
$\frac{4mg}{35}\times14a=\frac12m\times10ag-\frac12mV^2$
or
$\frac{4mg}{35}\times7a=mg\times7a\times\frac35-\frac12mV^2$
A1ft
A1ft
$V=\sqrt{\frac{34ag}{5}}$
Accept $2.6\sqrt{ag}$ , $\sqrt{6.8ag}$ , or better.

All question bank results loaded

Covered syllabus points

Question 1

Question (a)

Question (b)

Question 2

Question (a)

Question (b)