Ch 8.ppsx

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Tackle

Mighty Mike has a mass of 100 kg and is running down the football field at 4 m/s. Speedy Gonzales has a mass of 50 kg but runs 8 m/s, while Ponderous Poncho weighs

200 kg and runs only 2 m/s.

a) Speedy Gonzales b) Ponderous Poncho c) Both the same

Who is more likely to break his bones?

In the encounter, who will be more effective in

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Ch. 8: Momentum, Impulse and

Collisions

Newton’s Laws and Conservation of

Energy represent tools for solving

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(8.1) Momentum and Impulse

a

m

F





dt

v

d

m

F





(

m

v

)

dt

d



Note: p = mv is momentum with units kgm/s

dt

p

d

F





_{actually expressed his}*This is how Newton

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• _{a net force acting on an object causes a change in}

it’s momentum; better yet, net force = time rate of change of p

ex. air bags

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• _{if net force is constant, we can say}

t

p

F







p

t

F









Impulse of net force, J

p

J







p

₂



p

₁

Impulse-Momentum Theorem

an object’s change in p during a given time

interval equals the impulse of the net force acting during that time

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Example 8.2

Suppose you throw a ball with a mass of 0.4 kg

against a brick wall.

a) Find the impulse of the net force on the ball during its collision with the wall.

b) If the ball is in contact with the wall for 0.010 s, find the horizontal force that the wall exerts on the ball during the impact.

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Example 8.2

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Example 8.2

b) If the ball is in contact with the wall for 0.010 s, find the average horizontal force that the wall

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Impulse-Momentum Theorem

• _{all forces can be modeled by}

How do you calculate J exactly?

• _{to a good approximation,}

the average value of the force can be used to find the impulse

• _{in other words, these two}

areas are approximately equal







2 1 t t

dt

F

J

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Problem 8.11

Coach Johnson’s bat exerts a horizontal force on a 0.145-kg baseball given by

between t = 0 and t = 2.50 ms. At t = 0 the baseball’s velocity is .

i t s N t s N

F  [(1.60107 / )  (6.00109 / 2) 2]ˆ

s m j

iˆ 5.0ˆ) / 0

. 40

( 



a) Calculate the impulse exerted by the bat on the ball during the 2.50 ms that they are in contact.

b) Calculate the average force exerted by the bat on the ball during this time.

c) Calculate the momentum and velocity of the ball at t = 2.50 ms.

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• _{depending on the nature of a collision, the shape}

of F vs. t graph will vary

“hard”

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(8.2) Conservation of

Momentum

A

B

p

system=

isolated system (no external forces)

dt

p

d

F





2 1

p

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Example 8.5

Before After?

1. Find v_A₂_x

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Example 8.4

Recoil of a rifle

1. Find v_R_x

Why is there less recoil if you hold the rifle tight

against your shoulder?

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2. What are the final momentum and kinetic energy of the bullet? Of the rifle?

Example 8.4

Recoil of a rifle

Why the same? Why so different?

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Example 8.6

2D collision

Two robots are battling on a frictionless surface. Robot A, with mass 20 kg, initially

moves at 2 m/s parallel to the x-axis. It collides with robot B, which has mass 12 kg and is

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Example 8.6

2D collision

After the collision, robot A is moving at 1 m/s in a direction that makes an angle  = 30 with its initial direction. What is the final velocity of

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• _{in any collision (in which external forces can be}

neglected), p is conserved

• for elastic collisions: K_after = K_before

(collisions involving conservative forces, e.g. billiard balls, Rutherford’s experiment, cars with spring

bumpers or magnets)

• for inelastic collisions: K_after < K_before

(collisions involving non-conservative forces, e.g. cars crumpling in a crash, bullet embedding in wood block)

All real collisions are inelastic to some degree!

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What will happen in this elastic

collision?

before v

v/2

after v/2

after

ALWAYS OBSERVED!

v

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Example 8.7

Before

A completely inelastic collision

1. Find the common final velocity.

After?

2. Compare the initial and final kinetic energies.

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Example 8.8

A bullet, with mass m, is fired into a block of mass M, and makes a completely inelastic collision with it. After the impact of the bullet, the block swings up to a maximum height y.

Ballistic Pendulum

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b) Check answer with some realistic numbers:

m = 5 g M = 2 kg y = 3 cm

c) Compare initial and final kinetic energies?

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Example 8.10

An elastic collision

Before After

What are the velocities of A and B after the collision?

Note: Compare magnitude of relative velocity before

and after collision