# Force, work, power and energy

## Force, work, power and energy

A heavy wooden block is lying on a table. If you give it a gentle push, then it will move with a low velocity. In other words, if we apply a smaller force on the block, then its momentum changes slightly.

If you push the wooden block with a greater force, then the change in its momentum will be greater. Hence, we can conclude that the change in the momentum of a body is directly proportional to the strength of the applied force. This brings us to Newton’s second law of motion. It is stated as

The rate of change of momentum of an object is directly proportional to the unbalanced force acting on it. The direction of the unbalanced force is the same as the direction of the change of momentum.

Real world examples of Newton’s second law of motion

During an athletics event, the participants in the high jump event are provided with cushions to fall on after completing a jump. This is done to prevent any kind of injury to the athletes. When an athlete falls on the cushion, it takes him a longer period of time to

come to a stop. A small stopping force acts on the athlete because his rate of change of velocity is low. As a result, the athlete does not get hurt. If the athlete would have fallen on a hard surface, then his velocity would have been reduced to zero in a very short time. In this case, a large stopping force acts on the athlete because his rate of change of velocity is high. As a result, the athlete gets hurt.

A very useful application of this law lies in the use of seat belts in cars. To prevent injuries to passengers in the case of an accident, all cars are provided with seat belts. In the event of an accident, a fast moving car stops suddenly, i.e., its high velocity is reduced to zero in a very short interval of time. The time taken by the passengers to fall gets increased because of the seat belts worn by them. The rate of change of velocity of the passengers gets reduced because of the increase in the time taken by them to fall. Hence, a lesser stopping force acts on them as a result of which, injuries are reduced.

Mathematical formulation of Newton’s second law of motion

Consider a body of mass m. It initially moves with velocity u and accelerates at a constant rate a. It attains a final velocity v after time t. This acceleration is caused by force F. Now, Newton’s second law of motion can be mathematically represented as

You know that,

Using this, we obtain

F = ma = Mass × Acceleration

Thus, we can re-state Newton’s second law of motion as

Force acting on a body is equal to the product of its mass and acceleration.

If you push the wooden block with a greater force, then the change in its momentum will be greater. Hence, we can conclude that the change in the momentum of a body is directly proportional to the strength of the applied force. This brings us to Newton’s second law of motion. It is stated as

The rate of change of momentum of an object is directly proportional to the unbalanced force acting on it. The direction of the unbalanced force is the same as the direction of the change of momentum.

Real world examples of Newton’s second law of motion

**High Jump**During an athletics event, the participants in the high jump event are provided with cushions to fall on after completing a jump. This is done to prevent any kind of injury to the athletes. When an athlete falls on the cushion, it takes him a longer period of time to

come to a stop. A small stopping force acts on the athlete because his rate of change of velocity is low. As a result, the athlete does not get hurt. If the athlete would have fallen on a hard surface, then his velocity would have been reduced to zero in a very short time. In this case, a large stopping force acts on the athlete because his rate of change of velocity is high. As a result, the athlete gets hurt.

**Seat belts**A very useful application of this law lies in the use of seat belts in cars. To prevent injuries to passengers in the case of an accident, all cars are provided with seat belts. In the event of an accident, a fast moving car stops suddenly, i.e., its high velocity is reduced to zero in a very short interval of time. The time taken by the passengers to fall gets increased because of the seat belts worn by them. The rate of change of velocity of the passengers gets reduced because of the increase in the time taken by them to fall. Hence, a lesser stopping force acts on them as a result of which, injuries are reduced.

Mathematical formulation of Newton’s second law of motion

Consider a body of mass m. It initially moves with velocity u and accelerates at a constant rate a. It attains a final velocity v after time t. This acceleration is caused by force F. Now, Newton’s second law of motion can be mathematically represented as

You know that,

Using this, we obtain

F = ma = Mass × Acceleration

Thus, we can re-state Newton’s second law of motion as

Force acting on a body is equal to the product of its mass and acceleration.

**rajathadri**- LSF Member
- Posts : 25

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