Answer in Brief

**Answer the following question.**

One of the effects of a force is to change the momentum. Define the quantity related to this and explain it for a variable force. Usually, when do we define it instead of using the force?

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#### Solution

- Impulse is the quantity related to change in momentum.
- Impulse is defined as the change of momentum of an object when the object is acted upon by a force for a given time interval.

**Need to define impulse:**

- In cases when time for which an appreciable force acting on an object is extremely small, it becomes difficult to measure the force and time independently.
- In such cases, however, the effect of the force i.e, the change in momentum due to the force is noticeable and can be measured.
- For such cases, it is convenient to define impulse itself as a physical quantity.
- Example: Hitting a ball with a bat, giving a kick to a foot-ball, hammering a nail, bouncing a ball from a hard surface, etc.

**Impulse for a variable force:**

- Consider the collision between a bat and a ball. The variation of the force as a function of time is shown below. The force axis is starting from zero.
- From the graph, it can be seen that the force is zero before the impact. It rises to a maximum during the impact and decreases to zero after the impact.
- The shaded area or the area under the curve of the force-time graph gives the product of force against the corresponding time (Δt) which is the impulse of the force.

Area of ABCDE = F. Δt = impulse of force - For a constant force, the area under the curve is a rectangle.
- In case of a softer tennis ball, the collision time becomes larger and the maximum force becomes less keeping the area under the curve of the (F - t) graph the same.

Area of ABCDE = Area of PQRST

Concept: Impulse of a Force

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