9.3

Impulse

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The effect of force acting over a certain time can be represented by the derived quantity impulse. It is the product of force and the time interval over which the force is applied.

It is a vector quantity having the same direction as that of the force applied. It is expressed as vector J, and the SI unit is the newton-second.

If a graph is plotted between the net force and time, then impulse is given by the area under the curve, which is the definite integral of the force function over a time interval.

For instance, in golf, the ball experiences a large impulse during a slap shot. A huge force acts on the ball for less than a second which causes a change in the velocity of the ball.

The impulse of a large force acting over a shorter duration of time can be similar to that of a small force acting for a longer duration of time.

For instance, the impulse involved in stopping a truck either by sudden braking or by braking gently over a longer period of time would be similar.

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According to Newton’s second law of motion, the rate of change of the momentum of an object is the net external force acting on it. The total change in momentum between two timepoints thus depends on both the external force acting on it and the time over which it acts. Describing this mathematically, the total change of an object’s motion is proportional to the force vector and the time over which it is applied. This product is called impulse.

Additionally, it can be shown that the total impulse acting on an object over a time interval is equal to the average external force acting on it multiplied by the time interval. Hence, a measurement of the impulse helps calculate the average force that acts on an object during that interval. For example, approximately 50,000 years ago, a 25 meter iron-nickel meteorite collided with the Earth at about 12,800 meters per second in the northern Arizona desert in the United States. The impact created a large crater, approximately 1,200 meters in diameter and 170 meters deep, with a 45 meter high rim from the surrounding desert plain. Assuming that the impact lasted for a maximum of two seconds, it can be shown that the average force that the Earth applied on the meteorite during the collision was about 3 trillion newtons!

In another example, consider a person driving a car that has a frontal collision with a building and comes to rest. If the vehicle does not have an airbag, the driver collides with the car in a fraction of a second, and the force applied to the driver during this time is enormous. On the other hand, if the vehicle is fitted with an airbag, it increases the collision time. Hence, although the net change in motion of the driver is the same in both cases, the net force on the driver is lower, as it occurs over a greater time period. For this reason, airbags have become mandatory in all passenger vehicles in the United States since 1991, and they are increasingly common in Europe and Asia since the mid-1990s.

This text is adapted from Openstax, University Physics Volume 1, Section 9.2: Impulse and Collisions.

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