Question

20) Bob is pulling a 30kg filing cabinet with a force of 200N , but the filing cabinet refuses to move. The coefficient of static friction between the filing cabinet and the floor is 0.80.

Part A

What is the magnitude of the friction force on the filing cabinet?

Express your answer to two significant figures and include the appropriate units.

       f =      

Answer 1

Concepts and reason

The concepts required to solve the given question are force acting on a body and the effect of friction on the motion of the body and Newton’s third law.

Initially, find the magnitude of the frictional force acting on the filing cabinet from the mass, acceleration due to gravity and the coefficient of static friction. Then compare it with the force applied on the object. Finally, find the magnitude of the frictional force acting on the cabinet.

Fundamentals

Force acting on a body may be defined as the sudden push or pull which is capable of changing the direction of motion of the object, if it is unopposed.

Weight of an object is the “force of gravity”. It is defined as the mass times acceleration due to gravity.

Weight of the object is,

Here, W is the weight of the object, m is the mass of the object, and g is the acceleration due to gravity.

Normal force acting on the object is equal and opposite to the gravitational force applied on the object.

Frictional force is the resistive force which opposes the relative motion between the surfaces that are in contact with each other. It acts in the opposite direction of motion. There are mainly two types of frictional forces: static friction and dynamic friction.

Static frictional force can be calculated by taking the coefficient of friction between the two surfaces and multiplying it by the normal force that the surface applies on the object”. The normal force is equal to the force of gravity acting on the object, if it is on a flat surface.

Static frictional force can be expressed as,

Here, is the static frictional force, is the coefficient of static friction, and N is the normal force acting on the object.

Dynamic friction is defined as the “force that must be overcome to maintain steady motion of one body relatively to another as they remain constant.

(A)

Static frictional force:

Consider the expression for static frictional force,

Normal force is given by,

Substitute 30 kg for m and for g.

Hence the static frictional force is,

Substitute 0.8 for and 294 N for .

Force applied by the person on the filing cabinet,

The force is applied to the filling cabinet and the cabinet is stationary.

So, from Newton’s third law, the static frictional force on the filling cabinet is equal to the applied force.

Hence the magnitude of frictional force on the filing cabinet is,

Ans: Part A

Magnitude of the frictional force is .