Answer to Question #175866 in Classical Mechanics for Osama

Question

two particles A and B, of masses 3m and 4m respectively, attached to the ends of a light inextensible string. Initially A is held at rest on the surface of a fixed rough inclined plane. The plane is inclined to the horizontal at an angle x where tan(x) = 3/4 . The coefficient of friction between A and the plane is 1/4 . The string passes over a small smooth light pulley P which is fixed at the top of the plane. The part of the string from A to P is parallel to a line of greatest slope of the plane. The particle B hangs freely and is vertically below P. The system is released from rest with the string taut and with B at a height of 1.75 m above the ground. In the subsequent motion, A does not hit the pulley.

When B hits the ground, B does not rebound and comes immediately to rest.

Find the distance travelled by A from the instant when the system is released to the instant when A first comes to rest.

Answer 1

$$m_b gh=m_a g\sin{\alpha}l+\mu m_a gl\cos{\alpha}$$

$$\alpha=\arctan{\frac{3}{4}}=37\degree$$

$$(4)(1.75)=3(\sin{37}+0.25\cos{37})l\\l=2.91\ m$$