Chapter 8, Problem 4A

Distinguish between impact and impulse. Which designates a force and which is force multiplied by time?

To determine

To explain: The difference between impact and the impulse.

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

Explanation of Solution

Introduction:

The quantities impact and impulse are closely related to each other. The one aspect which separates them is the time of interaction. Impact signifies the interaction between two bodies and points towards the force between them, whereas impulse considers the effect of large force acting on a very short duration on a body.

When a body is in motion, it possesses a certain value of momentum and in order to change its momentum, an impact is necessary. This can be in the form of force during its interaction with another object, which can in turn reduce its initial momentum value. In this sense, the collision between two bodies can be treated as an impact between them and a force being exerted on one another. Here, the duration of the interaction is not playing a major role. The force of impact can be generally represented using Newton’s second law as,

  $F=ma$

Now, when a constant force F is applied on a body for a short duration t , then it produces an impulse, expressed as,

  $\text{Impulse}=Ft$

For an impulse, in terms of the example, if a constant and large force is applied on a cart for a specific time, the impulse considers the effect of such a force for this short duration.

The equation for impulse also suggests that even when the constant force is applied on an object for a longer duration, the impulse can increase.

Using impulse-momentum principle, the impulse can also be restated as the change in momentum expressed as,

  $Ft=m\Delta v$

The above relation follows from Newton’s second law which relates mass and acceleration.

From the above explanations, it can be understood that, the impact designates a force, whereas the impulse is the force multiplied by time.