We are solving problems based on the concept friction. It is a force acts opposite to relative motion. Frictional force is directly proportional to normal reaction. Normal reaction is the reaction acting on a body from the surface of contact normal to the surface. The proportionality is eliminated with a proportional constant and it is called coefficient of friction. It depends on the nature of the material and independent of normal reaction, weight of the body and force applied on the body.

**Problem**

It is given in the problem that a wooden block of mass M is resting on a horizontal surface and it is pulled with a force making an angle with the horizontal. If coefficient of kinetic friction is given to us, we need to measure the acceleration of the block. The problem is as shown in the diagram below.

**Solution**

Let the applied force is T and it can be resolved into components. The angle of inclination is given to us and we know the components acting in the horizontal and vertical directions. We know that the weight acts in the downward direction and we can find out the the total force acting in the down ward force acting by the block and the normal reaction is the same value in the opposite direction.

By writing the equation for the resultant force as the difference between the component of the applied force along the direction of motion and the frictional force, we can solve the problem as shown in the diagram below.

**Problem**

A person is holding a block of mass 2 kilogram between his two hands and he need to keep it with out falling vertically. If the force exerted by each hand is 50 newton, we need to know the coefficient of friction between the surface in contact.

**Solution**

We know that the applied force by hands acts like normal reaction and it is twice the applied force as it is applied with both the hands. Thus normal reaction is 100 newton. The weight of the body 20 newton acts in the downward direction and frictional force acts in the upward direction. Thus the product of efficient of friction and normal reaction is equal to the weight of the block acting in the opposite direction. Thus coefficient of friction is 0.2.

**Problem**

A body of mass 4 kilogram is initially kept at rest on a horizontal surface and coefficient of friction is given to us. A horizontal force is applied on the body and the distance covered in three seconds is given as 18 meter. We need to measure the ratio of applied force and the frictional force. The problem is as shown in the diagram below.

**Solution**

As the displacement is given to us, we can use second law of equation of motion and we can find the acceleration and thus the force the acting on the body. As coefficient of friction is also given to us, we can measure the frictional force acting and thus we can also find the effective force generated as shown below. The problem can be further solved as shown here.

**Problem**

It is given in the problem that under a certain force the body has some acceleration and when force is doubled, its acceleration is different. We need to find the coefficient of friction.

**Solution**

In each case, we can write the equation for the resultant force and we can equate it to the product of mass of the body and acceleration of each case. They can be further simplified and solved as shown below.

**Problem**

It is given in the problem that body is sliding on a horizontal surface and its contact force is double the frictional force. We need to find the coefficient of friction. The problem is as shown below.

**Solution**

Contact force is nothing but resultant force of normal reaction and fictional force and it can be found using the parallelogram law of vectors. By simplifying it further as shown below, the problem can be solved.

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