The diagram shows a particle of mass $$$5 \mathrm{~kg}$$$ on a rough horizontal table, and two light inextensible strings attached to it passing over smooth pulleys fixed at the edges of the table. Particles of masses $$$4 \mathrm{~kg}$$$ and $$$6 \mathrm{~kg}$$$ hang freely at the ends of the strings. The particle of mass $$$6 \mathrm{~kg}$$$ is $$$0.5 \mathrm{~m}$$$ above the ground. The system is in limiting equilibrium. In the subsequent motion the $$$8 \mathrm{~kg}$$$ particle hits the ground and does not rebound. Find the time that elapses after the $$$8 \mathrm{~kg}$$$ particle hits the ground before the other two particles come to instantaneous rest. (You may assume this occurs before either particle reaches a pulley.) .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w21_qp_43 Year：2021 Question No：6(c)

Answer:

$T-4 g=4 a,-T-F=5 a, F=2 g$ or $-4 g-2 g=9 a$
$a=-\frac{60}{9}$
$v^{2}=2 \times \frac{20}{17} \times 0.5=\frac{20}{17}$ leading to $v=\ldots[v=1.0846 \ldots]$
$0=\sqrt{\frac{20}{17}}-\frac{60}{9} t$
$t=0.163 \mathrm{~s}$

Knowledge points:

4.1.6 understand the concepts of limiting friction and limiting equilibrium, recall the definition of coefficient of friction, and use the relationship F = nR or F G nR, as appropriate

4.2.4 use appropriate formulae for motion with constant acceleration in a straight line. （Questions may involve setting up more than one equation, using information about the motion of different particles.）

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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