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 instead that the horizontal plane is rough and that when $$$P$$$ and $$$Q$$$ collide, they coalesce and move with speed $$$1.2 \mathrm{~m} \mathrm{~s}^{-1}$$$. Find the coefficient of friction between $$$P$$$ and the horizontal plane. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_41 Year：2020 Question No：7(b)

Answer:

$0.3 \times z+0=0.5 \times 1.2$
Velocity of $P$ before collision $z=2$
Friction force on $P$ after reaches horizontal plane $F=\mu \times 0.3 \mathrm{~g}$
$\mu \times 0.3 g \times 1.5=\frac{1}{2} \times 0.3 \times 5^{2}-\frac{1}{2} \times 0.3 \times 2^{2}$
Coefficient $\mu=0.7$
Alternative method for question 7(b)
$0.3 \times z+0=0.5 \times 1.2$
Velocity of $P$ before collision $z=2$
Friction force on $P$ after reaches horizontal plane $F=\mu \times 0.3 \mathrm{~g}$
$a=\left(5^{2}-2^{2}\right) /(2 \times 1.5)=7, F=0.3 \times 7$
Coefficient $\mu=0.7$

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.）

4.5.3 understand and use the relationship between the change in energy of a system and the work done by the external forces, and use in appropriate cases the principle of conservation of energy Including cases where the motion may not be linear (e.g. a child on a smooth curved ‘slide’), where only overall energy changes need to be considered.

Answer:

Knowledge points:

Solution:

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