Impulse & Momentum (Chapter 9 Part 1)

• New concepts: impulse & momentum

• Conservation of momentum

• Elastic vs inelastic collisions

2012 Nov 1Physics 130 - General Physics 1 - Fall 2012

• The units of momentum are kg m/s.

• Momentum is a vector, so it can be expressed in component form.

Linear momentum is the product of mass times velocity.

Recasting Newton’s second law in terms of momentum leads to the concept of impulse.

Rearranging and integrating:

We define the right-hand-side to be the impulse:

Impulse has a simple graphical interpretation.

Impulse equals the area under the Fx(t) curve between ti and tf.

Is impulse a vector?What are the units?

Impulse can also be found from the average force imparted during the collision.

Impulse imparted during the collision:

Below is a force-time curve for a golf ball struck by a club; what is the impulse delivered to the ball? What is the average force imparted?

• A rubber ball bounces off a wall.

• The ball initially travels to the right so both vix and pix are positive.

• After the bounce vfx and pfx are negative.

• The force on the ball is toward the left, so Fx is negative.

• Similarly, the impulse, or the area under the force curve, is negative.

Impulse-momentum theorem: the impulse delivered to a particle is equal to the change in its momentum.

Think-pair-share

A 2.0 kg object moving to the right with speed 0.50 m/s experiences the force shown. What are the object’s speed and direction after the force ends?

A. 0.50 m/s left

B. At rest

C. 0.50 m/s right

D. 1.0 m/s right

E. 2.0 m/s right

Think-pair-share

A 2.0 kg object moving to the right with speed 0.50 m/s experiences the force shown. What are the object’s speed and direction after the force ends?

A. 0.50 m/s left

B. At rest

C. 0.50 m/s right

D. 1.0 m/s right

E. 2.0 m/s rightΔpx = Jx or pfx = pix + Jx

Bar charts are one useful way to keep track of momentum changes.

• A ball moving to the right with pix=+2 kg m/s collides with a wall.

• The wall delivers an impulse of Jx=-4 N s.

• The final momentum is pfx=-2 kg m/s (moving to the left).

Think-pair-shareYou awake in the night to find that your living room is on fire. Your one chance to save yourself is to throw something that will hit the back of your bedroom door and close it, giving you a few seconds to escape out the window. You happen to have both a sticky ball of clay and a super-bouncy Superball next to your bed, both the same size and mass. You only have time to throw one. Which one will it be? Your life depends on making the right choice!

A. Throw the Superball.

B. Throw the ball of clay.

C. It doesn’t matter; throw either.

Think-pair-shareYou awake in the night to find that your living room is on fire. Your one chance to save yourself is to throw something that will hit the back of your bedroom door and close it, giving you a few seconds to escape out the window. You happen to have both a sticky ball of clay and a super-bouncy Superball next to your bed, both the same size and mass. You only have time to throw one. Which one will it be? Your life depends on making the right choice!

A. Throw the Superball.

B. Throw the ball of clay.

C. It doesn’t matter; throw either.

Larger Δp ⇒ more impulse to door

Example: hitting a baseball

Example 9.1 in Knight

• Draw a picture + coordinate system

• Identify the known & unknown quantities

• Draw a momentum bar chart

• Solve

Newton’s second and third laws lead to the Law of Conservation of Momentum

For an isolated system (net external force is zero):

Momentum is conserved in all collisions.

ElasticInelastic

Example: rolling away

Example 9.4 in Knight

• HW 9 on the first part of Chapter 9 due Friday 10/2 at 11PM

• Read the rest of Chapter 9 by Tuesday 11/6

• Chapter 9 Part 2 pre-class assignment due Tuesday 11/6 before class

Reminders