Two particles $$\(A\)$$ and $$\(B\)$$, of masses $$\(0.3 \mathrm{~kg}\)$$ and $$\(0.5 \mathrm{~kg}\)$$ respectively, are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley which is attached to a horizontal plane and to the top of an inclined plane. The particles are initially at rest with $$\(A\)$$ on the horizontal plane and $$\(B\)$$ on the inclined plane, which makes an angle of $$\(30^{\circ}\)$$ with the horizontal. The string is taut and $$\(B\)$$ can move on a line of greatest slope of the inclined plane. A force of magnitude $$\(3.5 \mathrm{~N}\)$$ is applied to $$\(B\)$$ acting down the plane (see diagram). Given that both planes are smooth, find the tension in the string and the acceleration of $$\(B\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_w20_qp_42 Year：2020 Question No：8(a)
Answer:
For \(A: T=0.3 a\)
For \(B: 3.5+0.5 g \sin 30-T=0.5 a\)
System: \(3.5+0.5 g \sin 30=(0.3+0.5) a\)
For solving either for \(T\) or for \(a\)
$
a=7.5 \mathrm{~ms}^{-2}
$
$
T=2.25 \mathrm{~N}
$
For \(B: 3.5+0.5 g \sin 30-T=0.5 a\)
System: \(3.5+0.5 g \sin 30=(0.3+0.5) a\)
For solving either for \(T\) or for \(a\)
$
a=7.5 \mathrm{~ms}^{-2}
$
$
T=2.25 \mathrm{~N}
$
Knowledge points:
4.1.1 identify the forces acting in a given situation； e.g. by drawing a force diagram.
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.
Solution:
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