It is given instead that the two planes are rough. When each particle has moved a distance of 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). $$$0.6 \mathrm{~m}$$$ from rest, the total amount of work done against friction is $$$1.1 \mathrm{~J}$$$. Use an energy method to find the speed of $$$B$$$ when it has moved this distance down the plane. [You should assume that the string is sufficiently long so that $$$A$$$ does not hit the pulley when it moves $$$0.6 \mathrm{~m}$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w20_qp_42 Year：2020 Question No：8(b)

Answer:

$0.5 g \sin 30 \times 0.6[=1.5]$
Apply the work-energy equation to the system
$0.5 g \sin 30 \times 0.6+3.5 \times 0.6=1 / 2 \times 0.8 \times v^{2}+1.1$
$v=2.5 \mathrm{~ms}^{-1}$

Knowledge points:

4.5.2 understand the concepts of gravitational potential energy and kinetic energy, and use appropriate formulae

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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