A car of mass $$$1250 \mathrm{~kg}$$$ is pulling a caravan of mass $$$800 \mathrm{~kg}$$$ along a straight road. The resistances to the motion of the car and caravan are $$$440 \mathrm{~N}$$$ and $$$280 \mathrm{~N}$$$ respectively. The car and caravan are connected by a light rigid tow-bar. The car and caravan now travel along a part of the road inclined at $$$\sin ^{-1} 0.06$$$ to the horizontal. The car and caravan travel up the incline at constant speed with the engine of the car working at $$$28 \mathrm{~kW}$$$ Find the increase in the potential energy of the caravan in one minute. ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_42 Year：2021 Question No：5(b)(ii)

Answer:

$ \mathrm{PE}=800 \mathrm{~g} \times d \times 0.06=800 \mathrm{~g} \times 14.4 \times 60 \times 0.06
$
$ \mathrm{PE}=414000(\mathrm{~J}) \text { or } \mathrm{PE}=414 \mathrm{~kJ}
$
Alternative method for Question 5(b)(ii)
$ \begin{array}{l}
28000 \times 60=\text { PE of Caravan }+1250 g \times d \times 0.06+720 \times d \\
\text { and } d=60 \times 14.359=861.54
\end{array}
$
$ \begin{array}{l}
{[\mathrm{PE}=28000 \times 60-1250 g \times 861.54 \times 0.06-720 \times 861.54]} \\
\mathrm{PE}=414000(\mathrm{~J}) \text { or } \mathrm{PE}=414 \mathrm{~kJ}
\end{array}
$

Knowledge points:

4.5.2 understand the concepts of gravitational potential energy and kinetic energy, and use appropriate formulae

Answer:

Knowledge points:

Solution:

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