A van of mass $$$3600 \mathrm{~kg}$$$ is towing a trailer of mass $$$1200 \mathrm{~kg}$$$ along a straight horizontal road using a light horizontal rope. There are resistance forces of $$$700 \mathrm{~N}$$$ on the van and $$$300 \mathrm{~N}$$$ on the trailer. The driving force exerted by the van is $$$2500 \mathrm{~N}$$$. Find the tension in the rope. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w21_qp_42 Year：2021 Question No：2(a)

Answer:

For van: $\quad 2500-700-T=3600 a$
For trailer: $\quad T-300=1200 a$
For system: $2500-700-300=(3600+1200) a$
Obtain an equation in $T$ only
$\left[a=\frac{5}{16}=0.3125\right]$
Tension in the rope $=T=675 \mathrm{~N}$

Knowledge points:

4.4.1 apply Newton’s laws of motion to the linear motion of a particle of constant mass moving under the action of constant forces, which may include friction, tension in an inextensible string and thrust in a connecting rod If any other forces resisting motion are to be considered (e.g. air resistance) this will be indicated in the question.

4.4.4 solve simple problems which may be modelled as the motion of connected particles. e.g. particles connected by a light inextensible string passing over a smooth pulley, or a car towing a trailer by means of either a light rope or a light rigid tow- bar.

Answer:

Knowledge points:

Solution:

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