## Monday, November 7, 2016

### Laws of Motion Problems with Solutions One

In the chapter laws of motion, we not only study how a body is moving, we also try to understand the forces acting on it who is causing the motion. Force is a physical quantity which change the state of the body or try to change the state of the body.

To study the motion of a body under the influence of the force, we have the famous three Newton's laws of motion. The first one is law of inertia, the second one is the law of force and the third one is law of action and reaction. We had discussed them in detail in the corresponding complete lesson Laws of motion.

Problem

It is given in the problem that a body of mass 2 kilogram is moving with a velocity and it is given in the vector format as shown below.A study force is applied on the body and it is also given in the form of a vector. We need to know, after four seconds what is the velocity of the body and in which direction it is moving.

Solution

We know that when a body has constant mass, force can be expressed as the product of mass and acceleration. So we can measure the acceleration of the body using that concept. We also know how to measure the final velocity of a body after a specific time using the definition of the acceleration as the rate of change of velocity. Thus we can measure the final velocity and finally basing on the component of the vector it has, we can identify the direction of velocity as shown below.

Problem

It is given in the problem that a constant force is acting on a body and we need to know the impulse acting on it in the first four seconds. The problem is as shown below.

Solution

Impulse is the large force acting on a body for a very short interval of the time. Many times this even cause the deformation in the shape of the body. We know that mathematically impulse and momentum are same. Any way by multiplying the force with time, we can get impulse as shown below. As it is required for a time interval of zero to  four seconds, we need to integrate between the given limits.

Problem

A horizontal force produces an acceleration on a block resting on a smooth horizontal surface. If the same force is applied on another body a different acceleration is produced. We need to measure the acceleration generated on a body when two blocks are tied together and the same force is applied on the combination. The problem is as shown in the diagram below.

Solution

We can solve the problem by applying the newton's second law of motion. We can find the relation between first mass and the second mass and by applying that relation, we can solve the problem as shown in the diagram below.

Problem

A constant force acts on a body of first mass and it produces a velocity and known displacement. The force is applied on a second body, a different velocity and displacement is generated. We need to find the ratio of the displacements. The problem is as shown in the diagram below.

Solution

We can solve the problem using the third equation of motion. So the product of displacement and acceleration is constant and we can solve the problem is as  shown below.

Problem

It is given that the impulse given to a body changes its velocity from one to other. We need to know the increase in the kinetic energy as shown in the diagram below.

Solution

We can rewrite the change in the kinetic energy as shown below. It can be expressed in terms of impulse as shown below.

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