A particle $$$P$$$ of mass $$$0.3 \mathrm{~kg}$$$ rests on a rough plane inclined at an angle $$$\theta$$$ to the horizontal, where $$$\sin \theta=\frac{7}{25}$$$. A horizontal force of magnitude $$$4 \mathrm{~N}$$$, acting in the vertical plane containing a line of greatest slope of the plane, is applied to $$$P$$$ (see diagram). The particle is on the point of sliding up the plane. The force acting horizontally is replaced by a force of magnitude $$$4 \mathrm{~N}$$$ acting up the plane parallel to a line of greatest slope. Find the acceleration of $$$P$$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_43 Year：2021 Question No：7(b)

Answer:

$F=\mu \times 0.3 g \cos \theta=\frac{3}{4} \times 3 \times \frac{24}{25} \quad\left[=\frac{54}{25}=2.16\right]$
$4-\frac{3}{4} \times 0.3 g \times \frac{24}{25}-0.3 g \times \frac{7}{25}=0.3 a$
$a=\frac{10}{3} \mathrm{~m} \mathrm{~s}^{-2}$

Knowledge points:

4.1.1 identify the forces acting in a given situation； e.g. by drawing a force diagram.

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.

4.1.4 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

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.

Answer:

Knowledge points:

Solution:

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