Two particles $$\(A\)$$ and $$\(B\)$$, of masses $$\(3 m \mathrm{~kg}\)$$ and $$\(2 m \mathrm{~kg}\)$$ respectively, are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley which is attached to the edge of a plane. The plane is inclined at an angle $$\(\theta\)$$ to the horizontal. $$\(A\)$$ lies on the plane and $$\(B\)$$ hangs vertically, $$\(0.8 \mathrm{~m}\)$$ above the floor, which is horizontal. The string between $$\(A\)$$ and the pulley is parallel to a line of greatest slope of the plane (see diagram). Initially $$\(A\)$$ and $$\(B\)$$ are at rest. It is given instead that the plane is rough, $$\(\theta=30^{\circ}\)$$ and the acceleration of $$\(A\)$$ up the plane is $$\(0.1 \mathrm{~m} \mathrm{~s}^{-2}\)$$. Show that the coefficient of friction between $$\(A\)$$ and the plane is $$\(\frac{1}{10} \sqrt{3}\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s20_qp_43 Year：2020 Question No：7(b)
Answer:
\(R=3 m g \cos 30\)
Use of \(F=\mu R\)
\(2 m g-T=0.1 \times 2 m\) OR \(T-3 m g \sin 30-\mu \times 3 m g \cos 30=0.1 \times 3 m\)
\(2 m g-0.2 m-3 m g \sin 30-\mu \times 3 m g \cos 30=0.1 \times 3 m\)
\(\mu=\frac{\sqrt{3}}{10}\)
Use of \(F=\mu R\)
\(2 m g-T=0.1 \times 2 m\) OR \(T-3 m g \sin 30-\mu \times 3 m g \cos 30=0.1 \times 3 m\)
\(2 m g-0.2 m-3 m g \sin 30-\mu \times 3 m g \cos 30=0.1 \times 3 m\)
\(\mu=\frac{\sqrt{3}}{10}\)
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.
4.4.1 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.
4.4.2 use the relationship between mass and weight W = mg. In this component, questions are mainly numerical, and use of the approximate numerical value 10 (m ) for g is expected.
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.
4.4.4 solve simple problems which may be modelled as the motion of connected particles. e.g. particles connected by a light inextensible string passing over a smooth pulley, or a car towing a trailer by means of either a light rope or a light rigid tow- bar.
Solution:
Download APP for more features
1. Tons of answers.
2. Smarter Al tools enhance your learning journey.
IOS
Download
Download
Android
Download
Download
Google Play
Download
Download