Impulse and Momentum: Understanding the Impulse-Momentum Theorem, Exams of Law

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Chapter 7

Impulse and Momentum

7.1 The Impulse-Momentum Theorem

There are many situations when the

force on an object is not constant.

7.1 The Impulse-Momentum Theorem

J = F! t

r r

7.1 The Impulse-Momentum Theorem

DEFINITION OF LINEAR MOMENTUM

The linear momentum of an object is the product

of the object’s mass times its velocity:

p v

r (^) r

= m

Linear momentum is a vector quantity and has the same

direction as the velocity.

kilogram !meter/second (kg! m/s)

7.1 The Impulse-Momentum Theorem

( ) f o

F v v

r r r

" t = m! m

final momentum initial momentum

IMPULSE-MOMENTUM THEOREM

When a net force acts on an object, the impulse of

this force is equal to the change in the momentum

of the object

impulse

7.1 The Impulse-Momentum Theorem

Example: Hitting a pitched baseball. A baseball of mass

0.14 kg is pitched at a batter with an initial velocity of

-38 m/s (negative is towards the bat). The bat applies an

average force that is much greater than the weight of the

ball, and the ball departs from the bat with a final velocity

of +58 m/s. Assuming that the time of contact with the bat

is 1.6 x 10

• s, find the average force exerted on the ball

by the bat.

f o

F v v

r r r

" t = m! m

= (0.14)(58) - (0.14)(-38) = +13.4 kg m/s

_

F = J /Δ t

= (13.4)/(1.6 x 10

• ) = +8400 N

J =

7.1 The Impulse-Momentum Theorem

Neglecting the weight of

the raindrops, the net force

on a raindrop is simply the

force on the raindrop due to

the roof.

f o

F v v

r r r

" t = m! m o

F v

r r

t

m

F =! ( 0. 060 kg s)(! 15 m s) = + 0. 90 N

r

7.1 The Impulse-Momentum Theorem

Conceptual Example: Hailstones Versus Raindrops

Instead of rain, suppose hail is falling. Unlike rain, hail usually

bounces off the roof of the car.

If hail fell instead of rain, would the force be smaller than, equal

to, or greater than that calculated in the previous Example?

7.2 The Principle of Conservation of Linear Momentum

Internal forces – Forces that objects within

the system exert on each other.

External forces – Forces exerted on objects

by agents external to the system.

The midair collision between two

objects.

7.2 The Principle of Conservation of Linear Momentum

f o

F v v

r r r

" t = m! m

1 12 1 f 1 1 o 1

W F v v

r r r r

• " t = m! m

2 21 2 f 2 2 o 2

W F v v

r r r r

• " t = m! m

OBJECT 1

OBJECT 2

External

forces

(gravity)

Internal

forces

7.2 The Principle of Conservation of Linear Momentum

The internal forces cancel out.

( ) f o P P

r r

sumof averageexternalforces " t =!

( ) f o

W W P P

r r r r

• " t =! 1 2

7.2 The Principle of Conservation of Linear Momentum

( ) f o P P

r r

sumof averageexternalforces " t =!

If the sum of the external forces is zero, then

f o P P

r r

0 =! f o P P

r r

=

PRINCIPLE OF CONSERVATION OF LINEAR MOMENTUM

The total linear momentum of an isolated system is constant

(conserved). An isolated system is one for which the sum of

the average external forces acting on the system is zero.

7.2 The Principle of Conservation of Linear Momentum

PRINCIPLE OF CONSERVATION OF LINEAR MOMENTUM

The total linear momentum of an isolated system is constant

(conserved). An isolated system is one for which the sum of

the average external forces acting on the system is zero.

In the top picture the net external force on the

system is zero.

In the bottom picture the net external force on the

system is not zero.

7.2 The Principle of Conservation of Linear Momentum

Applying the Principle of Conservation of Linear Momentum

1. Decide which objects are included in the system.
2. Relative to the system, identify the internal and external forces.
3. Verify that the system is isolated.
4. Set the final momentum of the system equal to its initial momentum.

Remember that momentum is a vector.