Edexcel IAL Maths M2.3.1 Work and Energy

[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

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

Edexcel A-Level Mathematics A2 M2.3.1 Kinetic and Potential Energy Work Questions

Exam points

Edexcel A-Level Mathematics A2 M2.3.1 Kinetic and Potential Energy Work Questions question 1

Question (a)

Question (b)