• You must complete at least 5 of the 6 labs to receive a passing grade in this course.

• If you missed a lab, you can make it up during one of two Review/Lab make-up weeks:

– October 24-28 (labs 1-3)– December 5-9 (labs 4-6)

• Even if you don’t need to make up a lab, you still must attend your section those weeks for the Review Recitation.

• To make up a lab, contact your TA ahead of time. You will need to arrange attending twice: (1) for lab make-up and (2) for the review recitation. You can attend any other section (in addition to your regular section), if you have that section’s TA permission in advance.

Section Next Week Reminder

Announcements• CAPA Set #9 due Friday at 10 pm

• CAPA Set #10 now available, due next Friday

• Next week in Section: See next slide

• Reading – Finish Chapter 7 on Momentum• Reading for next week – Chapter 8 on Rotation

• Next week Professor Uzdensky will give the lectures on rotational motion.• Nagle Monday office hours cancelled• Wednesday Help Room 1:45 – 3:45 pm by Uzdensky

m m

Consider a suspended blue sphere that collides elastically with a suspended red sphere.

vB

vA0

mm vB'0

vA'v

B

After impact, is the situation at right possible: A) Yes B) No

Clicker Question Room Frequency BA

Exactly as we derived for an elastic collision between two equal mass objects.

A bullet of mass m with unknown initial horizontal velocity v0 is fired into a large suspended block of mass M.

Ballistic PendulumClicker Question Room Frequency BA

Which of the following is true for the initial collision?A) Only energy is conserved B) Only momentum is conserved

C) Only kinetic Energy is conserved D) Energy and momentum are conserved

E) Kinetic energy and momentum are conserved

h

Clicker Question Room Frequency BA

For the initial collision where the bullet hits the pendulum, assuming no external work, can there be zero

thermal energy generated?A) Yes B) No

ffii PEKEPEKE ?

0)(2

10

2

1 220 vmMmv 0vmM

mv

vmMmv )(0 0vmM

mv

Impossible

h

Is the momentum of the system (M+m) conserved for the second part?

No, because an external net force is acting (gravity)!

We say so often the momentum is conserved, but it clearly cannot be if a

net external force is acting on the system.

Clicker Question Room Frequency BA

A) Yes B) No

ffii PEKEPEKE

ghmMvmM )(0)(2

1 2

g

vh

2

2

h

However, gravity is a conservative force and so mechanical energy is still conserved

(assuming no friction or air resistance).

A big ball of mass M = 10m and speed v strikes a small ball of mass m at rest.

Clicker Question Room Frequency BA

After the collision, could the big ball come to a complete stop and the small ball take off with speed 10 v?

A) Yes this can occurB) No, because it violates conservation of momentumC) No, because it violates conservation of energy

mvvmpinitial 10)10( mvvmp final 10)10(

22 5)10(2

1mvvmKEinitial

22 50)10(2

1mvvmKE final

Billiards

v 450

450

What is true about the speed of the red and white ball after?A) Equal Speeds, B) Red faster, C) White faster,

D) Cannot determine from the information given

Clicker Question Room Frequency BA

mvp initialx , )45cos()45cos( 21, mvmvp finalx

0, initialyp )45sin()45sin( 21, mvmvp finaly

Momentum is conserved (Δp = 0) if no net force operates during the interaction of two objects.

But, what if we only consider a single object or

if Fnet is non-zero?

Impulse

t

vmamFnet

vmtFnet

p

Impulse: ptFI net

= net force x time = change in momentum

I p

F

nettA ball bounces off the floor as

shown. The direction of the impulse of the ball, , is

A) Straight up,

B) Straight down,

C) To the right,

D) To the left,

E) Indeterminate.

p

v

1

v

2

θ θ

Note: the angle of incidence is equal to the angle of reflection.

p

1 p

p

2

Clicker Question Room Frequency BA

p

1 (px , py )

p

2 (px , py )

p p

2 p

1 (px , py ) (px , py )

= (0,2py )

A fast-ball thrown at a batter has a momentum of magnitude |pi| = (0.3kg)(40m/s) = 12 kg m/s.

The batter hits the ball back in a line drive with momentum of magnitude |pf| = (0.3kg)(80m/s) = 24 kg m/s.

What is the magnitude of the impulse |Δp|?

A) 12 kg m/sB) 24 kg m/sC) 36 kg m/sD) 0 kg m/sE) None of these.

I p

F

nettClicker Question Room Frequency BA

Pinitial = + 12 kg m/s

Pfinal = - 24 kg m/s

|Impulse|=|DP| = |-24 –(+12)|=36 kg m/s

Air Bags and ImpulseAbout 15 to 20 milliseconds after the collision occurs the crash

sensors decide whether or not the collision is serious enough to inflate the airbag (usually 6 - 10 km/h).

It takes about 20 milliseconds to inflate the airbag.

Around 60 milliseconds the person has made contact with the airbag and the airbag now starts to deflate.

The passenger continues to be acted on by the airbag as it is in the deflation process which takes about 35 to 40 milliseconds.

A 75kg man is involved in a car accident. He was traveling at 18 m/s (= 40 mph) when he hit a truck.

If he had no airbag in his car and he came to rest against the steering wheel in 50 milliseconds (0.05 seconds) find the force on his body.

Impulse = F Δt = Δp = m ΔvF = (m Δv) / Δt

F = (75kg)(-18m/s) / (0.05s)F = - 27,000 Newtons

If he had an airbag that inflated and deflated correctly, bringing him to rest over a time of 0.78s, find the force on his body.

F = (m Δv) / ΔtF = (75kg)(-18m/s) / (0.78s)

F = - 1,700 Newtons

Which is only about 6% of the force felt without an airbag… a definite improvement!

What is another benefit of the airbag in addition to a reduced force?

Distributing the force over a larger area also reduced injury (larger surface of contact with airbag compared to

just hitting the steering wheel).