Question

A Weightless inextensible rope rests on a stationary wedge forming an angle with the horizontal. One end of the rope is fixed to the wall at point A. A small load is attached to the rope at point B, The wedge starts moving with acceleration

Answer 1

"Given:

The figure is given which shows a weightless inextensible rope with wedge.

Solution:

Concept: “Draw the free body diagram based on equilibrium law of forces and then solve it using Lami’s theorem”.

The free body diagram of the given system is:

The acceleration of the load is based on the gravity and it is expressed as follows:

$a_{ B }=\sqrt { (a-acos\alpha )^{ 2 }+a^{ 2 }sin^{ 2 }\alpha } =a\sqrt { 1+cos^{ 2 }\alpha -2cos\alpha +sin^{ 2 }\alpha }$

$=\sqrt { 2-2cos\alpha } =\sqrt { 2\left( 1-cos\alpha \right) } =\sqrt { 2\times 2sin^{ 2 }\frac { \alpha }{ 2 } }$

$=2sin\frac { \alpha }{ 2 }$

Thus the acceleration of the load is $2sin\frac { \alpha }{ 2 }$"