1. Impulse-Momentum Lecture Notes

2. Definition of Momentum
Recall – Inertia
Inertia – A measure of a body’s resistance to a change in motion.
Mass
Momentum
Inertia in Motion
Product of an object’s mass and velocity.
Equation: p = mv
Momentum is a vector quantity.
Units – kgm/s

3. Example #1
Calculate the momentum of a 1200 kg truck traveling at 35 m/s east.
G: m = 1200 kg
v = 135 m/s
U: p = _________
E: p = mv
S: See Overhead

4. Example #2
How fast must an ordinary housefly travel to have a momentum equal to that of the truck? The average housefly has a mass of 1 gram.
G: mtruck = 1200 kg
vtruck = 135 m/s
mfly = 1 g
U: v = ________
E: p = mv
S: See Overhead

5. Definition and Equation for Impulse
Pre Lab Impulse Lab
Bungee Jump Lab
Definition and Equation for Impulse

6. Post Lab Impulse Lab Bungee Jump Lab
What was the impact of rebounding on the Impulse?

7. Relate Impulse to Force vs. Time Graphs
What quantity is related to the slope of the graph?

8. Revisit Newton’s Second Law of Motion
Fnet = ma
a = v/t
Fnet = mv/t
Fnett = mv
Fnett = m(vfinal – vinitial)
Fnett = mvfinal – mvinitial
Fnett = pfinal – pinitial
Fnett = p

9. Definition Impulse-Momentum Theorem
Fnett = p….
Impulse = Change in Momentum
Impulse = Fnett
Impulse = The product of the average net force and time over which it acts on an object.
Units – Ns
Change in Momentum = p
Change in Momentum = The product of an object’s mass and its change in velocity.
Units – kg m/s

10. Example #3
A particle moves along the x-axis. Its momentum is graphed to the right as a function of time. Rank the numbered regions according to the magnitude of the net force acting on the particle, least to greatest.
Fnett = p
Fnet = p/t
Fnet = slope
Magnitude = Steepness

11. Example #4
A bug collides with the windshield of a fast moving truck. Qualitatively analyze each of the following statements.
splat
The forces of impact on the bug and on the truck are the same. 
The impulses on the bug and on the truck are the same.
The changes in velocity of the bug and of the truck are the same.
The changes in momentum of the bug and of the truck are the same.

12. Impulse-Momentum Example #5
What impulse will give a 0.15-kg baseball a momentum change of + 50 kgm/s?
G: m = 0.15 kg
Dp = 50 kgm/s
U: impulse
E: FDt = Dp
S: See Overhead

13. Example #6
A 0.05 kg golf ball is dropped from the window of a building. It strikes the sidewalk below at 30 m/s and rebounds up at 20 m/s. What’s the magnitude of the impulse due to the collision with the sidewalk? What’s the change in momentum of the ball as a result of the collision with the sidewalk? What is the average net force exerted on the golf ball if the collision took seconds?
G: m = 0.05 kg
vo = 30 m/s
v = 20 m/s
Dt = s
U: Favg
E: FDt = Dp
S: See Overhead S: See Overhead

14. Example #7
A 2-kg object is acted upon by a single force in the x direction in a manner described by the graph shown. What’s the change in the object’s momentum? What is the object’s final velocity if it started from rest? Calculate the average force applied to the object.
Impulse = area under the curve

15. Revisit Newton’s Third Law of Motion
Fnet = – Fnet
Fnett = – Fnett
Fnett = p
p = – p
pf – pi = –(pf – pi)
pf – pi = –pf + pi
pf + pf – pi – pi = 0
pf + pf – (pi + pi) = 0
pf – pi = 0
psystem = 0
Momentum is Conserved

16. Collision - Elastic
A cue ball, mass 200 grams, moves with a velocity of 20.0 cm/s. It collides head-on with a stationary 8-ball, mass 200 grams. After the collision the cue comes to rest. What’s the velocity of the 8-ball? Prove this is an elastic collision.
G: mcue = 200 g m8-ball = 200 g
vocue = 20.0 cm/s vo8-ball = 0
vcue = 0
U: v8-ball
E: p = mv
S: See Overhead

17. Collision - Inelastic
A 90 kg fullback running at 10 m/s collides head-on with a 120 kg defensive tackle running at 3 m/s. The fullback knocks the tackles backwards and continues running at 5 m/s. Whatis the velocity of the tackle after the collision?
G: mfull = 90 g mtackle = 200 g
vofull = 10 m/s vo8tackle = 3 m/s
vfull = 5 m/s
U: vtackle
E: p = mv
S: See Overhead

18. Collision - Inelastic
A hockey puck, mass 0.10 kg, moving at 32 m/s, strikes an octopus thrown on the ice by a fan at a Detroit Red Wings game. The octopus has a mass of 0.30 kg. The puck and octopus slide off together. Find their velocity.
G: mpuck = 0.10 kg moctopus = 0.30 kg
vopuck = 32 m/s vooctopus = 0
U: v
E: p = mv
S: See Overhead

19. Collision - Recoil
Two spacemen are floating together with zero speed in a gravity-free region of space. The mass of spaceman A is 120 kg and that of spaceman B is 80 kg. Spaceman A pushes B away from him with B attaining a final speed of 0.5 m/s. Calculate the final recoil speed of A.
G: mA = 120 kg mB = 80 kg
voA = 0 voB = 0
vB = 0.5 m/s
U: vA
E: p = mv
S: See Overhead

20. Kinetic Energy Conserved
Collision Chart
Momentum Conserved
Energy Conserved
Kinetic Energy Conserved
Elastic
Inelastic
Recoil
Yes
Yes
Yes
Yes No
Yes No
Yes
Yes