• 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

• This week in Section: Lab #3 – Momentum

• Reading – Chapter 7 on Momentum

Kind of like kinetic energy (associated with motion).

However, not in units of Joules (instead kg m/s) and so not an energy.

In addition to total energy being conserved in every collision, the total momentum vector is also conserved!

momentum p

mv (a vector)

p

1i p

2i p

1 f p

2 f Conservation of Momentum

mv1i mv2i mv1 f mv2 f (in one-dimension)

New Conserved Quantity Momentum

In which situation is the magnitude of the total momentum the largest?

A) Situation I.B) Situation II.C) Same in both.

ptotal = mv + 0 = mv

Clicker Question Room Frequency BA

ptotal = mv-2mv=-mv

Magnitudes are the same |ptotal|=mv

An object of mass m1 initially moving with speed v1i collides with another object of mass m2 initially at rest.

The objects stick together after the collision.

m1 m2

v1i v2i=0

Totally Inelastic Collision

What is the velocity of the objects after the collision?

m1 m2

vf

Before

After

ffii vmvmvmvm 22112211 fi vmmvm )(0 2111

if vmm

mv 1

21

1

Does that

make sense?

m1 m2

v1i v2i=0m1 m2

vf

v f m1

m1 m2

v1i

Totally Inelastic CollisionIs Kinetic Energy conserved?

Before After

021 2

11 ii vmKE 221 )(

21

ff vmmKE

From momentum conservation

21

2

21

121 )(

21

if vmm

mmmKE

21

12112

1mm

mvmKE if

21

1

mmm

KEKE if

Kinetic Energy Decreases(not conserved)

Elastic Collision ExampleAn object of mass m initially moving with speed v

collides with another object of mass m initially at rest.

m1 m2

v v2i=0 Before

For an elastic collision, what happens afterwards?

finalinitial pp Momentum Conserved

ff mvmvmv 210 One equation, two unknowns

(v1f & v2f)

Kinetic Energy Conserved

22

21

2

21

210

21

ff mvmvmv

Now we have two equations, two

unknowns (v1f & v2f)

ff mvmvmv 21 22

21

2

21

21

21

ff mvmvmv

ff vvv 21 22

21

2ff vvv

ff vvv 21 plug in

22

22

2 )( ff vvvv 22

222

22 2 fff vvvvvv 222 22 ff vvv

vv f 2

ff vvv 21 01 fv

m1 m2

v1i v2i=0 Before

m1

v1f=0 Afterm2

V2f

Is that really correct?

Demonstration….

Why is Momentum Conserved?During the collision, Newton’s Third Law applies.

F21 = - F12

m2 a2= - m1a1

Assume a constant acceleration when the objects are in contact for a time Dt

tvv

tva if

D

DD

D

D

tvv

mtvv

m ifif 222

111

iiff vmvmvmvm 22112211 Momentum conservation resulting from Newton 2nd + 3rd Law

Two masses of size m and 3m are at rest on a frictionless table.

A compressed, massless spring between the masses is suddenly allowed to uncompress, pushing the masses apart.

After the masses separate, the speed of m is _______ the speed of 3m.A) the same as B) twice C) 3 times D) 4 times

v1v2

1 2

Clicker Question Room Frequency BA

21 30 mvmv finalinitial pp

21 3vv

Two masses of size m and 3m are at rest on a frictionless table.

A compressed, massless spring between the masses is suddenly allowed to uncompress, pushing the masses apart.

After the masses separate, the KE of m is _______ the KE of 3m.A) the same as B) twice C) 3 times D) 9 times

-3v v1 2

Clicker Question Room Frequency BA

221 2

9)3(21 mvvmKE 22

2 23)3(

21 mvvmKE

Two masses of size m and 3m are at rest on a frictionless table.

A compressed, massless spring between the masses is suddenly allowed to uncompress, pushing the masses apart.

While the spring is in contact with the masses, how does the magnitude of the force of m on 3m compare to the

magnitude of the force of 3m on m?A) the same as B) less thanC) greater than D) unknown

-3v v1 2

Clicker Question Room Frequency BA

A cannon of mass M=1000 kg fires a cannonball of mass m=10 kg with velocity vB=100m/s.

What is the recoil velocity vC of the cannon?

finalinitial pp Momentum is conserved

BC mvMv 0

BC vMmv

smsmkgkgvC /1/100

100010

What happens to keep the cannon from going back at 1m/s?

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