Impulse & Momentum
From Newton 2:
• Previously: Work-Energy
SF=ma
multiply both sides by d
 S F d= m a d (note a d = ½ Dv2)
 S F d= ½ m Dv2
 S W = DKE
 Define Work and Kinetic Energy
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From Newton 2:
Two New Concepts
Impulse & Momentum
Fnet  ma
Dv
Fnet  m
Dt
Fnet  Dt  m  Dv
Impulse
N-s
Change In
Momentum
Kg m/s
I  Fnet  Dt
Impulse = Change in Momentum
Momentum; p  mv
Momentum is vector in direction
of velocity.
Impulse is vector in direction of
force.
m
N  s  kg 
s
Preflight 1
A few weeks ago I did a lecture demonstration
where I yanked a tablecloth out from under some
dishes. Can you briefly explain why the dishes were
not given much impulse by the tablecloth.
Impulse is defined as force time the change in time. If the change in
time is very small, the impulse is going to be small.
The dishes just didn’t feel like moving…
The cloth may have been made out of a slick material (i.e. silk) so
the friction is negligible…
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Preflight 2 & 3
Is it possible for a system of two objects to have zero total
momentum while having a non-zero total kinetic energy?
67%
1. YES
33%
2. NO
correct
yes, when two objects have the same mass and velocities and they push off
each other..momentum is zero and kinetic energy is nonezero.
2 balls traveling at the same speed hit
each other head-on.
Change in Momentum ACT
If the bear and the ball have equal masses, which toy
experiences the greater change in momentum?
Change in momentum: Dp = pafter - pbefore
Teddy Bear:
Dp = 0-(-mv) = mv
Bouncing Ball: Dp = mv-(-mv) = 2mv
Change in Momentum ACT2
A 10 kg cart collides with a
wall and changes its
direction. What is its change
in x-momentum Dpx?
y
x
a. -30 kg m/s
b. -10 kg m/s
c. 10 kg m/s
d. 20 kg m/s
e. 30 kg m/s
ACTs
You drop an egg onto 1) the floor 2) 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
same impulse
In which case is the average force greater
A) Floor
Dp = F Dt
B) Foam
F = Dp/Dt
C) the same
Smaller Dt = larger F
Pushing Off…
Fred (75 kg) and Jane (50 kg) are at rest on skates facing
each other. Jane then pushes Fred w/ 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
Fred
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 / 75 kg
= 1.8 m/s
C) Jane
Jane
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 / 50 kg
= -2.7 m/s
Note: Pfred + Pjane = (1.8) 75 + (-2.7) 50 = 0!
Momentum Change ACT
A car w/ 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:
Pfinal – Pinitial = (0 – 48000) = -48,000 kg m/s
30 m/s
East-West:
Pfinal – Pinitial = (36000 - 0) = +36,000 kg m/s
Magnitude :
Sqrt(P2North – P2East ) = 60,000 kg m/s
40 m/s
Impulse and Momentum
Summary
FaveDt  I = pf - pi = Dp
• For single object….
• F = 0  momentum conserved (Dp = 0)
• For collection of objects …
• SFext = 0  total momentum conserved (DPtot = 0)
• Fext = mtotal a
• 4. •• IP Two air track carts move toward one another on an air
track. Cart 1 has a mass of 0.45 kg and a speed of 1.1 m/s. Cart 2
has a mass of 0.65 kg. (a) What speed must cart 2 have if the total
momentum of the system is to be zero? (b) Since the momentum of
the system is zero, does it follow that the kinetic energy of the
system is also zero? (c) Verify your answer to part (b) by calculating
the system’s kinetic energy.
• 9. • In a typical golf swing, the club is
in contact with the ball for about
0.0010 s. If the 45-g ball acquires a
speed of 67 m/s, estimate the
magnitude of the force exerted by the
club on the ball.
•
•
• 5. •• A 0.150-kg baseball is dropped from rest. If the
magnitude of the baseball’s momentum is just before it
lands on the ground, from what height was it dropped?