A particle of mass $$$12 \mathrm{~kg}$$$ is stationary on a rough plane inclined at an angle of $$$25^{\circ}$$$ to the horizontal. A force of magnitude $$$P \mathrm{~N}$$$ acting parallel to a line of greatest slope of the plane is used to prevent the particle sliding down the plane. The coefficient of friction between the particle and the plane is $$$0.35$$$. Find the least possible value of $$$P$$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w21_qp_41 Year：2021 Question No：4(b)

Answer:

Attempt to resolve forces parallel to the plane
$P+F=12 g \sin 25[=50.7]$
$R=12 g \cos 25 \quad[=108.8]$
$F=120 \cos 25 \times 0.35 \quad[=38.1]$
$P+38.1=120 \sin 25$
$P=12.6$

Knowledge points:

4.1.2 understand the vector nature of force, and find and use components and resultants； Calculations are always required, not approximate solutions by scale drawing.

4.1.3 use the principle that, when a particle is in equilibrium, the vector sum of the forces acting is zero, or equivalently, that the sum of the components in any direction is zero （Solutions by resolving are usually expected, but equivalent methods (e.g. triangle of forces, Lami’s Theorem, where suitable) are also acceptable; these other methods are not required knowledge, and will not be referred to in questions.）

4.1.4 understand that a contact force between two surfaces can be represented by two components, the normal component and the frictional component

4.1.6 understand the concepts of limiting friction and limiting equilibrium, recall the definition of coefficient of friction, and use the relationship F = nR or F G nR, as appropriate

Answer:

Knowledge points:

Solution:

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