## SAT Physics Momentum and Impulse - Momentum

MOMENTUM
There are two types of momentum, linear momentum and angular momentum. The SAT Subject Test in Physics is restricted to problems involving linear momentum, the momentum of objects moving in a straight-line path.

Linear Momentum
Linear momentum is the product of the mass and velocity of an object.
Momentum has units of kilograms • meters per second. Momentum is related to the inertia of a moving object. The greater the momentum of a moving object, the more difficult the object is to stop. Momentum is a vector quantity. The direction of the momentum vector is the same as the direction of the velocity of the object.

Total Momentum
Many problems involve a system (more than one object) moving simultaneously. The total momentum of a system can be found by adding the individual momentums of all the objects making up the system.
Note that momentum and velocity are both vector quantities. Vector direction for one-dimensional motion can be annotated with a positive or a negative sign as shown in the formula below.
By adding plus and minus signs, the vector velocity, v, becomes a scalarlike quantity, v, allowing simple addition. You must note the direction of velocity and add the correct sign when solving a problem for momentum.

IMPULSE
Impulse is a force that is applied to an object over a period of time. A kick or a shove would be considered an impulse.
From this equation, the units of impulse will be newton • seconds (N • s). This is also equiva­lent to the units of momentum, kg • m/s. Both momentum and impulse can be expressed in either of these units. Impulse is a vector quantity, and the impulse vector points in the direc­tion of the force acting on the object.
When analyzing the equation for impulse, it is apparent that if the duration of a collision can be lengthened, the force of the impact can be lessened. For example, air bags in an automobile are designed to increase the amount of time needed for a passenger to come to a complete stop, thereby decreasing the force exerted on the passenger during a collision.

Impulse-Momentum Theorem
When an impulse acts on an object, the momentum of the object will change. Note that impulse does not equal momentum even though their units are the same. Impulse causes and is equal to the change in the momentum of an object. Impulse is similar to work (dis­cussed in the previous chapter) in that they both create a change. Work changes the energy of a mass, and impulse changes the momentum of a mass. Impulse and work are both processes of change, while momentum and energy are both state functions.

Change In Momentum
(A) Determine the change in momentum (impulse) for a 0.5-kilogram lump of clay striking a wail at 15 meters per second.

WHAT'S THE TRICK?

The lump of clay will stick to the wall, and come to a stop.
The negative sign in the answer indicates that the change in momentum is opposite the initial velocity. The minus sign may not appear in the available answer choices since problems of this type are often concerned with just the value.
(B) Determine the change in momentum (impulse) for a 0.5-kilogram rubber ball striking a wall at 15 meters per second and bouncing off the wall in the opposite direction.

WHAT'S THE TRICK?

The rubber ball will bounce off of the wall. Unless told otherwise, assume that the final speed of the ball leaving the wall is the same as the initial speed of the ball.
Note the minus sign on the final velocity of the ball. Set the initial velocity as positive. Since the ball reversed direction during the bounce, the final velocity is in the opposite direction and it must have the opposite sign.
The change in momentum (impulse) for an object that bounces with no loss in speed is twice as large as the change in momentum for an object coming to a stop.

Force-Time Graph
Impulse is equal to the area under a force versus time function. The graph in Figure 8.1(a) left is an example of the impulse delivered to a soccer ball when the ball is kicked. However, this graph will probably appear in the simplified form of Figure 8.1(b) to allow you to calculate the area under the function with ease.
In the graphs in Figure 8.1, the force is continually changing. Therefore, the formula for impulse requires you to find the average force, Favg, delivered during the time interval, Δt. The magnitude of impulse in the graph on the right is:

Figure 8.1. Force-time graphs
You can solve for impulse in a variety of ways. Impulse is equal to:

The most challenging problems may require you to set one formula for impulse equal to another.

Impulse

The above graph illustrates the force acting on a 0.20-kilogram soccer ball as it is kicked. Determine the final speed of the ball.

WHAT'S THE TRICK?

A force-time graph indicates that this problem involves impulse. You can solve an impulse problem in many possible ways.
You need a method that lets you use the graph to solve for speed. The above formula can be simplified to include speed and the area of a triangle.
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