Chapter 8, Problem 6A

Distinguish between impulse and momentum. Which is $\text{force}\times \text{time}$ and which is inertia in motion?

To determine

To explain: The difference between impulse and momentum.

To find: The quantity that represents force multiplied by time and that represents inertia in motion.

Explanation of Solution

Introduction:

The momentum of a body represents its resistance to change its state of motion and can be expressed as the product of mass and velocity of the body,

  $\text{Momentum}=mv$

When a force F is applied on a body for a particular duration t , then it produces an impulse, expressed as,

  $\text{Impulse}=Ft$

As evident from the definition of momentum, changing the momentum of a body requires the application of a force. And this in turn depends on the mass of the body.

For example, the momentum of a truck is much higher than the momentum of a bicycle. This signifies the effect of inertia or resistance to move even when same force is applied on both the objects.

Now, in most of the cases, the mass is constant and a force applied on a body puts it into acceleration. But, as in the example, since a truck has a larger mass than the bicycle, same force cannot set them into motion. So, here to create acceleration, the force has to be applied for a longer duration on the truck.

For example, when a force is applied on the truck, the impulse implies the duration for which the force is being applied on the cart while it is set into motion.

The force to be applied can be expressed using the Newton’s second law as,

  $F=ma$

Since acceleration represents rate of change of velocity of the body with time, the above equation can be rearranged as,

  $F=m\frac{\Delta v}{\Delta t}$

Rearranging the above equation leads to the relation,

  $F\Delta t=m\Delta v$

Here, the term on the left-hand side represents an impulse and the term on the right side represents the change in momentum of the body. This is the impulse-momentum principle and this implies that impulse causes a change in momentum.

From the above explanations, it can be understood that, momentum designates inertia in motion, whereas the impulse is the force multiplied by time which can change the momentum.