Momentum & ImpulseExcerpts from

Chapters 9 and 11

Impulse and MomentumNewton’s 2nd Law of motion can be rewritten

by using the definition of acceleration as the change in velocity over the change in time.

F ma

F m vt

Impulse and MomentumIf the change in time is multiplied out of the

denominator, we are left with the following:

Ft mv

Ft mvThe product of force and change in

time is called the impulse (symbol is J).

Impulse is a vector quantity and is measured in Newton-seconds (Ns).

ImpulseIf a car hits a haystack or the same car hits a

wall, momentum is decreased by same impulse – the same products of force and time.

However, impact force is greater into the wall than it is into the haystack as the haystack extends impact time, lessening the impact force.

Impact time is the time during which momentum is brought to zero.

mvThe product of the mass and the

velocity is called the momentum (symbol -“rho”) of an object.

Momentum is also a vector quantity and is measured in kgm/s.

Note that the units for impulse and momentum appear different, but they are actually the same unit when simplified.

MomentumMomentum can be increased with an

increase in either mass or in velocity or both. Ex: a rolling bowling ball has greater

momentum than a tennis ball rolling at the same speed because its mass is greater

Ex: a racecar going forward at 120 mi/hr has greater momentum than the same size car going 90 mi/hr due to its greater velocity

If an object is not moving (no matter how big it is), the momentum is equal to zero.

Ft mv f mviThe impulse-momentum theorem

states that the impulse on an object is equal to the object’s final momentum minus the object’s initial momentum.

Can also be written as:

Ft f i

Example 1Tiger Woods hits a 0.050kg golf ball,

giving it a speed of 75m/s. What is the impulse given to the ball?

Example 1 Answer

m0.050kgv 75m /simpulse?

Ft mvimpulse 0.050 75impulse 3.75 3.8N s

Example 2Shane hits a stationary 0.12kg hockey

puck with a force that lasts for 1.0x10-2s and makes the puck shoot across the ice with a speed of 20.0m/s, scoring a goal for the team. With what force did Shane hit the puck?

Example 2 Answer

m0.12kg

t 1.0 10 2sv 20.0m /sF ?

Ft mv

F mvt

F 0.12 20.01.0 10 2

F 240N

Example 3Diana, whose mass is 50.0kg, leaves a

ski jump with a velocity of 21.0m/s. What is her momentum as she leaves the ski jump?

Conservation of MomentumA system is the environment and all of

the objects examined in a problem.A closed system is a system in which no

mass is gained or lost.An isolated system is a system in which

the net external force is zero… no forces acting outside of the system have an effect inside of it.

Conservation of MomentumThe law of conservation of momentum states that

the sum of momentum of any closed, isolated system does not change… or that the sum of the momentum of the objects in that system is constant.

Conservation of MomentumMathematically, we can view this as a BEFORE

and AFTER situation.For any two objects A and B:

Ai Bi Af Bf

Types of Collisions If two objects bounce apart when they collide, it is called an

elastic collision and can be written:

If two objects stick together when they collide, it is called

an inelastic collision and can be written:

m1v1i m2v2i m1v1 f m2v2 f

m1v1i m2v2i (m1 m2)v f

Example 1Tubby and his twin brother Chubby

have a combined mass of 200.0kg and are zooming along in a 100.0kg amusement park bumper car at 10.0m/s. They bump Melinda’s car, which is sitting still. Melinda has a mass of 25.0kg. After the elastic collision, the twins continue ahead with a speed of 4.12m/s. How fast is Melinda’s car bumped across the floor?

Example 1 Picture

MelT&C

m1 300.0kgv1i 10.0m /s

m2 125.0kgv2i 0m /s

Before Collision

MelT&C

m1 300.0kgv1 f 4.12m /s

m2 125.0kgv2 f ?

After Collision

Example 1 Answer

m1v1i m2v2i m1v1 f m2v2 f

m1v1i m2v2i m1v1 f m2v2 f

m1v1i m2v2i m1v1 f

m2

v2 f

Example 1 Answer

[m1v1i m2v2i m1v1 f ]m2

v2 f

[(300.010.0) (125.00) (300.04.12)]125.0

v2 f

14.1m /sv2 f

Example 2If an 800.kg sports car slows to

13.0m/s to check out an accident scene and the 1200.kg pick-up truck behind him continues traveling at 25.0m/s, with what velocity will the two move if they lock bumpers after a rear-end collision?

Example 2 Picture

m1 1200.kgv1i 25.0m /s

m2 800.kgv2i 13.0m /s

Before Collision

(m1 m2) 2000.kgv f ?

After Collision

Example 2 Answer

m1v1i m2v2i (m1 m2)v f(m1v1i m2v2i)

(m1 m2)v f

Example 2 Answer

(m1v1i m2v2i)(m1 m2)

v f

[(120025.0) (80013.0)](1200 800)

v f

20.2 m/s forward v f

Journal #What do we mean when we ask people to

“conserve water”?

What do you think it will mean if we say that momentum is conserved?

Conservation LabObjective:

Prove that the law of conservation of momentum is true.

Law of Conservation of Momentum:The sum of the momentum of the objects

prior to a collision is equal to the sum of the momentum of the objects after a collision.

Journal #Explain how an airbag protects you

by making you come to a stop differently than hitting steering wheel.Try to use the words impulse, force, and time in your

answer.

Journal #Impulse is a force applied over an

interval of time. In this question, the impulse of hitting the steering wheel and hitting the airbag are the same amount because they both cause you to stop. However, the airbag applies a smaller force to your body over a larger time, therefore keeping you safer.

Journal # Order these objects from the most momentum

to the least.A. A bullet shot from a rifleB. An elephant standing still C. A bowling ball rollingD. A fly buzzing by your ear