What is MOMENTUM?

Units: kg m/s

Newton’s 2nd Law written in terms of change in momentum

What is IMPULSE?

Units: N s

Force

Timearea = I

Time

Force Force on a car versus time for a typical car collision.

BOXING AND BRAIN INJURYBare fists were used in the past, now fighters wear padded gloves.

Why?

Other examples with the same application:

Car bumpers, Air bags, Seat belt

From Newton’s 2nd Law:

Impulse-Momentum Theorem

1. the car2. the truck3. the change in the magnitude of momentum is

the same for both4. impossible to determine without more

information

A car and a large truck traveling at the same speed collide head-on and stick together. Which vehicle undergoes the larger change in the magnitude of its momentum?

Quick Quiz

Impulse-Momentum Theorem

Force when the bodies are in contact

Velocities before and after the contact (no contact is happening)

The same force F is applied to different bodies originally at rest for different amounts of time. The diagrams below show the results (after the force ceased).

m

3m

m

2m

m

x0 = 0

3.0v

2.5v

1.0v

1.5v

Rank the IMPULSE for each diagram from the greatest IMPULSE to the least IMPULSE applied.

(A)

(B)

(C)

(D)

(E)

Quick Quiz

Collision of astronauts

During a collision (only while the objects are in touch) the objects receive an

IMPULSE (I)t F I

Impulse on astronaut 2

Impulse on astronaut 1

I1I2

IMPULSE HAPPENS DURING THE COLLISION

Units of Impulse

I = [ N . s](3)

Bouncing Ball

Conservation of momentum

Two skaters of different masses prepare to push off against one another. Which one

will gain the larger velocity?a) The more massive oneb) The less massive onec) They will each have equal

but opposite velocities.The net external force acting on the system is zero, so conservation of momentum applies.Before the push-off, the total initial momentum is zero.The total momentum after the push-off should also be zero.

Collisions

Glancing collisions

Two lumps of clay of equal mass are traveling at right angles with equal speeds

as shown, when they collide and stick together. Is it possible that their final

velocity vector is in the direction shown?a) yesb) noc) unable to tell

from this graph

No. The final momentum will be in a direction making a 45o degree angle with respect to each of the initial momentum vectors.

Two cars of equal mass Collide at right angles to one another in an intersection.

Their direction of motion after the collision is as shown. Which car had the greater

velocity before the collision? a) Car Ab) Car Bc) Their velocities were

equal in magnitude.d) It is impossible to tell

from this graph.

Since the angle with respect to the original direction of A is smaller than 45º, car A must have had a larger momentum and thus was traveling faster.