Question

In the given figure a monkey of mass m is climbing a rope hanging from the roof with acceleration a. The coefficient of static friction between the body of the monkey and the rope is $\mu $. Find the direction and value of friction on the monkey.

Answer 1

Hint: When two bodies are kept in contact, electromagnetic force act between charged particles at the surface of the bodies. As a result, each body exerts a force on the other body.

Complete step by step answer:
Given, a monkey of mass $m$ is climbing a rope hanging from the roof with acceleration $a$, the coefficient of static friction between the body of the monkey and the rope is $\mu $.
The coefficient of static friction depends on the nature of the surface it is in contact with.
If there is no friction between the monkey and the rope then the monkey would fall down. Therefore, the frictional force helps the monkey to climb. Hence, friction is in an upward direction.

Force acting in a downward direction is weight and upward direction is friction.
Since the net force is in an upward direction.
Therefore, $ma = F - mg$
$ \Rightarrow F = ma + mg$
$\therefore F = m(a + g)$

The value of friction on the monkey is $F = m(a + g)$ in upward direction.

Note:
Friction is defined as the opposing force which comes into play tangentially between two surfaces so as to destroy the relative motion between them. A surface appears smooth by seeing in the naked eye, but when we see microscopically, we can find many numbers of irregularities. When two bodies are placed one above the other, these surface irregularities interlock together and oppose any changes of relative motion between the bodies.
Safe walking on the floor nails and screws are held in the walls, helps the fingers to hold drinking water, vehicles move on the roads without slipping all these are advantages of friction.
The wear and tear of the machinery parts, heating of the machinery parts, large amount of power loss in the engine all these are disadvantages of friction.