## SAT Physics Subject Test

## Chapter 5 Linear Momentum

### IMPULSE

The product of force and the time during which it acts is known as **impulse,** a term you should be familiar for this test.

**That Hurts!**

Since concrete is hard and

has no cushion, this makes

the impact time of any

object striking concrete

very short. Forces that

exist over a short period of

time are called impulsive

forces. A large change in

momentum divided by a

short time interval makes

for a painful landing on a

concrete floor.

Impulse is a vector quantity that”s symbolized by **J**.

J = ∆*t*

Newton”s second law can be written in yet another form, in terms of impulse.

**J** = ∆**p**

Sometimes this is referred to as the **impulse–momentum theorem**, but it”s just another way of writing Newton”s second law.

2. A football team”s kicker punts the ball (mass = 0.42 kg) and gives it a launch speed of 30 m/s. Find the impulse delivered to the football by the kicker”s foot and the average force exerted by the kicker on the ball, given that the impact time is 0.0020 s.

Here”s How to Crack It

Impulse is equal to the change in linear momentum, so

*J* = ∆*p* = *p*_{f} – *p*_{i} = *p*_{f} = *mv* = (0.42 kg)(30 m/s) = 13 kg × m/s

Using the equation , we find that the average force exerted by the kicker is

**Questions 3-5**

An 80 kg stuntman jumps out of a window that”s 45 m above the ground.

3. How fast is he falling when he reaches ground level?

4. He lands on a large, air-filled target, coming to rest in 1.5 s. What average force does he feel while coming to rest?

5. What if he had instead landed on the ground (impact time = 10 ms) ?

Here”s How to Crack It

3. His gravitational potential energy turns into kinetic energy: *mgh* = *mv*^{2}, so

(You could also have answered this question using Big Five #5.)

4. Using = ∆p/∆*t*, we find that

5. In this case

**Time**

Seconds are represented

in questions as s. If you

see a quantity that refers

to time labeled with ms,

it is using milliseconds.

Because impact happens

so quickly, a smaller

quantity of time is

necessary.

This force is equivalent to about 27 tons(!), more than enough force to break bones and cause fatal brain damage. Notice how crucial the impact time is: Increasing the slowing-down time reduces the acceleration and the force, ideally enough to prevent injury. This is the purpose of safety devices such as air bags in cars.

6. A small block is struck by a force **F** whose strength varies with time according to the following graph:

What is the impulse delivered to the block?

Here”s How to Crack It

The impulse delivered to the block is equal to the area under the curve. The region is a triangle, so its area, base × height, can be calculated as follows: