# 8.2 Impulse

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• Define impulse.
• Describe effects of impulses in everyday life.
• Determine the average effective force using graphical representation.
• Calculate average force and impulse given mass, velocity, and time.

The effect of a force on an object depends on how long it acts, as well as how great the force is. In [link] , a very large force acting for a short time had a great effect on the momentum of the tennis ball. A small force could cause the same change in momentum    , but it would have to act for a much longer time. For example, if the ball were thrown upward, the gravitational force (which is much smaller than the tennis racquet’s force) would eventually reverse the momentum of the ball. Quantitatively, the effect we are talking about is the change in momentum $\Delta \mathbf{p}$ .

By rearranging the equation ${\mathbf{F}}_{\text{net}}=\frac{\Delta \mathbf{p}}{\Delta t}$ to be

$\Delta \mathbf{p}={\mathbf{F}}_{\text{net}}\Delta t,$

we can see how the change in momentum equals the average net external force multiplied by the time this force acts. The quantity ${\mathbf{F}}_{\text{net}}\Delta t$ is given the name impulse    . Impulse is the same as the change in momentum.

## Impulse: change in momentum

Change in momentum equals the average net external force multiplied by the time this force acts.

$\Delta \mathbf{p}={\mathbf{F}}_{\text{net}}\Delta t$

The quantity ${\mathbf{F}}_{\text{net}}\Delta t$ is given the name impulse.

There are many ways in which an understanding of impulse can save lives, or at least limbs. The dashboard padding in a car, and certainly the airbags, allow the net force on the occupants in the car to act over a much longer time when there is a sudden stop. The momentum change is the same for an occupant, whether an air bag is deployed or not, but the force (to bring the occupant to a stop) will be much less if it acts over a larger time. Cars today have many plastic components. One advantage of plastics is their lighter weight, which results in better gas mileage. Another advantage is that a car will crumple in a collision, especially in the event of a head-on collision. A longer collision time means the force on the car will be less. Deaths during car races decreased dramatically when the rigid frames of racing cars were replaced with parts that could crumple or collapse in the event of an accident.

Bones in a body will fracture if the force on them is too large. If you jump onto the floor from a table, the force on your legs can be immense if you land stiff-legged on a hard surface. Rolling on the ground after jumping from the table, or landing with a parachute, extends the time over which the force (on you from the ground) acts.

## Calculating magnitudes of impulses: two billiard balls striking a rigid wall

Two identical billiard balls strike a rigid wall with the same speed, and are reflected without any change of speed. The first ball strikes perpendicular to the wall. The second ball strikes the wall at an angle of $\text{30º}$ from the perpendicular, and bounces off at an angle of $\text{30º}$ from perpendicular to the wall.

(a) Determine the direction of the force on the wall due to each ball.

(b) Calculate the ratio of the magnitudes of impulses on the two balls by the wall.

Strategy for (a)

In order to determine the force on the wall, consider the force on the ball due to the wall using Newton’s second law and then apply Newton’s third law to determine the direction. Assume the $x$ -axis to be normal to the wall and to be positive in the initial direction of motion. Choose the $y$ -axis to be along the wall in the plane of the second ball’s motion. The momentum direction and the velocity direction are the same.

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