### SAT Physics Momentum and Impulse - Momentum

## 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.

**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.

**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.

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.

**(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.

**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, F

_{avg}, delivered during the time interval, Δt. The magnitude of impulse in the graph on the right is:

**Figure 8.1. Force-time graphs**

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

**Impulse**

**WHAT'S THE TRICK?**

A force-time graph indicates that this problem involves impulse. You can solve an impulse problem in many possible ways.

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