Two particles $$$P$$$ and $$$Q$$$ of masses $$$0.5 \mathrm{~kg}$$$ and $$$m \mathrm{~kg}$$$ respectively are attached to the ends of a light nextensible string. The string passes over a fixed smooth pulley which is attached to the top of two inclined planes. The particles are initially at rest with $$$P$$$ on a smooth plane inclined at $$$30^{\circ}$$$ to the horizontal and $$$Q$$$ on a plane inclined at $$$45^{\circ}$$$ to the horizontal. The string is taut and the particles can move on lines of greatest slope of the two planes. A force of magnitude $$$0.8 \mathrm{~N}$$$ is applied to $$$P$$$ acting down the plane, causing $$$P$$$ to move down the plane (see diagram). It is given that $$$m=0.3$$$, and that the plane on which $$$Q$$$ rests is smooth. Find the tension in the string. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_m21_qp_42 Year：2021 Question No：7(a)

Answer:

Attempt Newton's 2 nd law for either $P, Q$ or the system.
For $P: \quad 0.8+0.5 g \sin 30-T=0.5 a$
For $Q: \quad T-0.3 g \sin 45=0.3 a$
System: $\quad 0.8+0.5 g \sin 30-0.3 g \sin 45=0.8 a$
Attempt to solve for $T$.
$T=2.56 \mathrm{~N}(3 \mathrm{sf})$

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.

4.4.3 solve simple problems which may be modelled as the motion of a particle moving vertically or on an inclined plane with constant acceleration Including, for example, motion of a particle on a rough plane where the acceleration while moving up the plane is different from the acceleration while moving down the plane.

Answer:

Knowledge points:

Solution:

Related Question