A particle $$$P$$$ of mass $$$0.4 \mathrm{~kg}$$$ is on a rough horizontal floor. The coefficient of friction between $$$P$$$ and the floor is $$$\mu$$$. A force of magnitude $$$3 \mathrm{~N}$$$ is applied to $$$P$$$ upwards at an angle $$$\alpha$$$ above the horizontal, where $$$\tan \alpha=\frac{3}{4}$$$. The particle is initially at rest and accelerates at $$$2 \mathrm{~m} \mathrm{~s}^{-2}$$$. Find $$$\mu$$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_m20_qp_42 Year：2020 Question No：2(b)

Answer:

$R=0.4 g-3 \times \frac{3}{5}=0.4 g-3 \sin 36.9[=2.2]$
$\left[3 \times \frac{4}{5}-F=3 \cos 36.9-F=0.4 \times 2\right] \quad[F=1.6]$
$\left[\mu=\frac{3 \times \frac{4}{5}-0.4 \times 2}{0.4 g-3 \times \frac{3}{5}}=\frac{1.6}{2.2}\right]$
$\mu=0.727$

Knowledge points:

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

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

4.4.1 apply Newton’s laws of motion to the linear motion of a particle of constant mass moving under the action of constant forces, which may include friction, tension in an inextensible string and thrust in a connecting rod If any other forces resisting motion are to be considered (e.g. air resistance) this will be indicated in the question.

Answer:

Knowledge points:

Solution:

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