1. Purdue University, Physics 220
Lecture 12
Momentum and Impulse
Lecture 11
Purdue University, Physics 220

2. Purdue University, Physics 220
Obama’s Momentum
Lecture 11
Purdue University, Physics 220

3. Purdue University, Physics 220
Impulse and Momentum
Define Momentum
Momentum is a VECTOR
Define Impulse
Change in momentum requires Force acting over a period of time or Impulse
Dp = FDt or I = Dp
Impulse: F t Vector Momentum transfer
Work: Fr r Scalar Energy transfer
Do some collisions to motivate idea
Lecture 11
Purdue University, Physics 220

4. Purdue University, Physics 220
Impulse and Momentum
I  Ft = pf - pi = p
impulse-momentum theorem
For single object …
F = 0  momentum conserved (p = 0)
For collection of objects …
ptotal = p
Internal forces: forces between objects in system
External forces: all other forces
Fext = 0  total momentum conserved (ptot = 0)
Lecture 11
Purdue University, Physics 220 1

5. Purdue University, Physics 220
1-D F vs t Plot
Impulse is simply the area under the
Fx(t) curve!
Lecture 11
Purdue University, Physics 220

6. Purdue University, Physics 220
iClicker
By what factor does an object’s kinetic energy change if its speed is doubled? By what factor does the magnitude of the momentum change?
A) 0.5, 4
B) 2, 2
C) 4, 2
Lecture 11
Purdue University, Physics 220

7. Purdue University, Physics 220
Pushing Off…
Fred and Jane are on skates facing each other. Jane then pushes Fred with force F
N2L Fred: FJF = mFred aFred
DvFred = aFred Dt
= (FJF/mFred) Dt
mFred DvFred = FJF Dt
N2L Jane: FFJ = mJane aJane
DvJane = aJane Dt
= (FFJ/mJane) Dt
mJane DvJane = FFJ Dt
N3L: For every action, there is an equal and opposite reaction. FFJ=-FJF
mFred DvFred = -mJane DvJane
a = v/t
Do some collisions to motivate idea
Lecture 11
Purdue University, Physics 220

8. Purdue University, Physics 220
Pushing Off…
Fred (75 kg) and Jane (50 kg) are on skates facing each other. Jane then pushes Fred with a constant force F = 45 N for a time Dt=3 seconds.
Who will be moving fastest at the end of the push?
A) Fred B) Same C) Jane
Jane
F = +45 [N] (positive direct.)
I = +45  3 [N*s] = 135 [N*s]
I = Dp
= mvf – mvi
I/m = vf - vi
vf = 135 [N*s] / 50 [kg]
= 2.7 [m/s]
Fred
F = -45 [N] Newton’s 3rd law
I = -45  3 [N*s] = -135 [N*s]
I = Dp
= mvf – mvi
I/m = vf - vi
vf = -135 [N*s] / 75 [kg]
= -1.8 [m/s]
Note: pFred + pJane = (1.8) (-2.7) 50 = 0!
Lecture 11
Purdue University, Physics 220

9. Purdue University, Physics 220
Momentum is Conserved
Define Momentum p = m v
m1 Dv1 = -m2 Dv2
Dp1 = -Dp2
Dp1+p2) = Dp = 0
pinitial = pfinal
Example: Jane pushes Fred so he is going 2.0 m/s. If Fred is twice as heavy as Jane, how fast does Jane end up moving.
0 = mFred vFred + mJane vJane
vJane = -mFred vFred / mJane = -4 m/s
Momentum is conserved p1f-p1i+p2f-p2i=0
p1f+p2f=p1i+p2i
Do some collisions to motivate idea
Lecture 11
Purdue University, Physics 220

10. Purdue University, Physics 220
Momentum is a Vector
A car with mass 1200 kg is driving north at 40 m/s, and turns east driving 30 m/s. What is the magnitude of the car’s change in momentum?
A) 0 B) 12,000 C) 36,000 D) 48,000 E) 60,000
pinitial = m vinitial = (1200 kg) x 40 m/s = 48,000 kg m/s North
pfinal = m vfinal = (1200 kg) x 30 m/s = 36,000 kg m/s East
North-South:
pNSfinal – pNSinitial = (0 – 48000) = -48,000 kg m/s
East-West:
pEWfinal – pEWinitial = ( ) = +36,000 kg m/s
40 m/s
30 m/s
Magnitude:
Sqrt(pNS2 + pEW2 ) = 60,000 kg m/s
Lecture 11
Purdue University, Physics 220

11. Purdue University, Physics 220
Soft vs Hard Impact
You drop an egg onto A) the floor B) a thick piece of foam rubber. In both cases, the egg does not bounce.
In which case is the impulse greater?
A) Floor
B) Foam
C) the same
I = Dp
Same change in momentum
In which case is the average force greater
A) Floor
B) Foam
C) the same
Dp = F Dt
F = Dp/Dt
smaller Dt -> large F
Lecture 11
Purdue University, Physics 220

12. Purdue University, Physics 220
Bouncy vs Sticky Ball
Two identical balls are dropped from the same height onto the floor. In each case they have velocity v downward just before hitting the floor. In case 1 the ball bounces back up, and in case 2 the ball sticks to the floor without bouncing. In which case is the magnitude of the impulse given to the ball by the floor the biggest?
A) Case 1
B) Case 2
C) The same
p=mv = mat = Ft = I
Bouncing Ball
|I| = |Dp|
= |mvfinal – m vinitial|
= |m( vfinal - vinitial)|
= 2 m v
Sticky Ball
|I| = |Dp|
= |mvfinal – m vinitial|
= |m(0 - vinitial)|
= m v
Might Add numbers here.
Lecture 11
Purdue University, Physics 220

13. Purdue University, Physics 220
Bouncy vs Sticky Ball
Two identical balls are dropped from the same height onto the floor. In case 1 the ball bounces back up, and in case 2 the ball sticks to the floor without bouncing. In both cases of the above question, the direction of the impulse given to the ball by the floor is the same. What is this direction?
A) Upward
B) Downward
time
Lecture 11
Purdue University, Physics 220

14. Purdue University, Physics 220
Question
Two objects are known to have the same kinetic energy. Do these two objects necessarily have the same momentum?
A) Yes
B) No
Lecture 11
Purdue University, Physics 220

15. Purdue University, Physics 220
iClicker
At the instant a bullet is fired from a gun, the bullet and the gun have equal and opposite momenta. Which object has the greater kinetic energy?
A) The same
B) The gun
C) The bullet
Apply conservation of momentum:
Pi= Pf=MgunVgun+mbulletvbullet
Vgun=-(mbullet/Mgun)vbullet
Lecture 11
Purdue University, Physics 220

16. Purdue University, Physics 220
Outline
We have learned: Work-Energy Theorem
F = m a multiply both sides by Dx
F Dx = m a Dx (note: aDx = ½ Dv2)
F Dx = ½ m Dv2
W = DK Defines Work and Kinetic Energy
We will learn: Impulse-Momentum Theorem
F = m a multiply both sides by Dt
F Dt= m a Dt (note: aDt = Dv)
F Dt= m Dv
I = Dp Defines Impulse and Momentum
Lecture 11
Purdue University, Physics 220

17. Purdue University, Physics 220
Newton’s Second Law
New formulation of Newton’s 2nd Law
Lecture 11
Purdue University, Physics 220 1