## Monday, November 14, 2016

### Friction Problems and Solutions One

Friction is a force that opposes the relative motion between two bodies that are in contact. It is because of molecular force of attraction between among the molecules are in contact. If the two bodies are at rest the friction between them is called static friction and if one is in motion, then it is called kinetic friction. If a body is rolling, it is called rolling friction. To measure the friction,  we need to use coefficient of the friction and it is different for each type of the friction.

Problem

It is given in that a force of 12 newton is acting on a body of mass 4 kilogram and the body is on a rough surface of known coefficient of the friction. We need to measure the acceleration of the body. The problem is as  shown in the diagram below.

Solution

When we apply certain force on a body, it tries to change its position along the direction of the applied force and and hence the frictional force acts in the opposite direction.

We can measure the resultant force as the difference between the applied force and the frictional force. We can measure the acceleration of the system as shown below.

Problem

It is given in the problem that a body of mass 2 kilogram is placed on a horizontal surface and the coefficient of static and kinetic frictions were given. If a horizontal force is applied on a body, we need to measure the frictional force acting on the body. The problem is as shown below.

Solution

The applied force is only 2.5 newton. Coefficient of static friction is given to us and we can measure the maximum static frictional force as the the product of normal reaction and coefficient of friction. As per the given data, the maximum static frictional force is 10 newton and the applied force is less than that. So the applied force is less than the maximum static frictional force and hence the body continuous in the same state of the rest. The static frictional force self adjusts itself to the applied force. The solution is as shown in the diagram below.

Problem

A train consisting of 30 wagons and each ones mass is given to us. The power of the engine pulling the train is also given to us in the problem. Frictional force per each tonne is given as 12 newton and we need to measure the maximum velocity of the train.

Solution

Total mass of the train is the product of number of wagons and mass of each one. Total frictional force can be found as the product of friction per tonne and the total mass in tonne. We can define power as the rate of change of  work done and the dot product of frictional force and velocity. Using this concept, we can solve the problem as shown in the diagram below.

Problem

A pulling force with a known angle is applied on the body with vertical of block known weight. If the angle of friction is given to us, we need to measure the force required to move the body. The problem is as shown in the diagram below.

Solution

We can understand that the applied force can be resolved into components and one component is helping to move the body and the other turned as the part of the normal reacting. We can write the equation for resultant force and solve the problem as shown below.

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