Two particles $$\(A\)$$ and $$\(B\)$$, of masses $$\(3 m \mathrm{~kg}\)$$ and $$\(2 m \mathrm{~kg}\)$$ respectively, are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley which is attached to the edge of a plane. The plane is inclined at an angle $$\(\theta\)$$ to the horizontal. $$\(A\)$$ lies on the plane and $$\(B\)$$ hangs vertically, $$\(0.8 \mathrm{~m}\)$$ above the floor, which is horizontal. The string between $$\(A\)$$ and the pulley is parallel to a line of greatest slope of the plane (see diagram). Initially $$\(A\)$$ and $$\(B\)$$ are at rest. When $$\(B\)$$ reaches the floor it comes to rest. Find the length of time after $$\(B\)$$ reaches the floor for which $$\(A\)$$ is moving up the plane. [You may assume that $$\(A\)$$ does not reach the pulley.] ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s20_qp_43 Year：2020 Question No：7(c)
Answer:
$
v^{2}=0+2 \times 0.1 \times 0.8 \quad(v=0.4)
$
\(-3 m g \sin 30-\mu \times 3 m g \cos 30=3 m a(a=-6.5)\)
\(0=-0.4-6.5 t\)
$
t=0.4 / 6.5=0.0615 \mathrm{~s}
$
v^{2}=0+2 \times 0.1 \times 0.8 \quad(v=0.4)
$
\(-3 m g \sin 30-\mu \times 3 m g \cos 30=3 m a(a=-6.5)\)
\(0=-0.4-6.5 t\)
$
t=0.4 / 6.5=0.0615 \mathrm{~s}
$
Knowledge points:
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.
4.4.3 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.
Solution:
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