particle $$\(P\)$$ of mass $$\(0.3 \mathrm{~kg}\)$$, lying on a smooth plane inclined at $$\(30^{\circ}\)$$ to the horizontal, is released from rest. $$\(P\)$$ slides down the plane for a distance of $$\(2.5 \mathrm{~m}\)$$ and then reaches a horizontal plane. There is no change in speed when $$\(P\)$$ reaches the horizontal plane. A particle $$\(Q\)$$ of mass $$\(0.2 \mathrm{~kg}\)$$ lies at rest on the horizontal plane $$\(1.5 \mathrm{~m}\)$$ from the end of the inclined plane (see diagram). $$\(P\)$$ collides directly with $$\(Q\)$$. It is given that the horizontal plane is smooth and that, after the collision, $$\(P\)$$ continues moving in the same direction, with speed $$\(2 \mathrm{~m} \mathrm{~s}^{-1}\)$$. Find the speed of $$\(Q\)$$ after the collision. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s20_qp_41 Year：2020 Question No：7(a)
Answer:
\(0.3 g \sin 30=0.3 a(a=5)\)
(M1 for applying Newton's second law parallel to the plane)
\(v^{2}=0+2 \times 2.5 \times a\)
\(v=5\)
\(0.3 \times 5+0=0.3 \times 2+0.2 w\)
Velocity of \(Q=4.5 \mathrm{~ms}^{-1}\)
(M1 for applying Newton's second law parallel to the plane)
\(v^{2}=0+2 \times 2.5 \times a\)
\(v=5\)
\(0.3 \times 5+0=0.3 \times 2+0.2 w\)
Velocity of \(Q=4.5 \mathrm{~ms}^{-1}\)
Knowledge points:
4.3.2 use conservation of linear momentum to solve problems that may be modelled as the direct impact of two bodies. （Including direct impact of two bodies where the bodies coalesce on impact. Knowledge of impulse and the coefficient of restitution is not required.）
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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