Momentum
Physics I
FoxTrot: Bill Amend
Momentum Defined
Momentum p is defined as the product of mass andvelocity, mv. Units: kg m/s
p = mv
p = mv
Momentum
m = 1000 kg
v = 16 m/s
p = (1000 kg)(16 m/s)
p = 16,000 kg m/s
p = 16,000 kg m/s
Author: Tippens, P. (2007)
IMPULSE
t
F
J = F t
J = F t
Impulse:
Impulse J is a force Facting for a small timeinterval t.
Author: Tippens, P. (2007)
Example 1: The face of a golf club exerts anaverage force of 4000 N for 0.002 s. What isthe impulse imparted to the ball?
t
F
Author: Tippens, P. (2007)
What is the unit for Impulse?Derive the unit from the equation.
Ans: 8 Ns
The average force acting over an interval of timegives the same impulse as the actual force.
Impulse
Normally, a forceacting for a shortinterval is notconstant. It maybe large initiallyand then play offto zero as shownin the graph.
Impulse from a Varying Force
Impulse Changes Velocity
Consider a mallet hitting a ball:
F
Impulse = Change in “mv”
Impulse = Change in “mv”
Author: Tippens, P. (2007)
Hailstone vs. Raindrop
Which exerts a larger impulse on the car?
Which exerts a larger force on the car?
Explain.
Hailstone
Hailstone
Impulse and Momentum
Impulse = Change in momentum
F t = mvf - mvo
F t = mvf - mvo
t
F
mv
A force F acting on a ball for a timet increases its momentum mv.
Author: Tippens, P. (2007)
The Physics Classroom. [Animations].
Vector Nature of Momentum
Consider the change in momentum of a ball that is droppedonto a rigid plate:
vo
vf
A 2-kg ball strikes the plate with a speed of 20m/s and rebounds with a speed of 15 m/s.What is the change in momentum?
+
Author: Tippens, P. (2007)
Impluse Sample Problem
An 18,000 kg bus is moving with a speed of 15 m/s. IfSuperman is to stop the bus in 5 seconds, what averageforce must he exert on the bus?
Explain why Superman’sforce is negative?
Your Turn!A 500-g baseball moves to the left at 20 m/s strikinga bat. The bat applies a force of 5000 N on the ball ,and it leaves in the opposite direction at 40 m/s.What was the time of contact?
40 m/s
t
F
20 m/s
m = 0.5 kg
+
-
+
Author: Tippens, P. (2007)
Pause forPractice
Ans: 0.006 sec
Bellringer Questions
You have 2 minutes to answer the following questions.
1.Momentum is a __ quantity.
A. ScalarB. vector
2. If you increase the time of impact, then you can ___the amount of force when applying an impulse.
A. IncreaseB. decreaseC. not change
3.A 2 kg mass moves right with a speed of 1 m/s andrebounds with a speed of 2 m/s. What is thechange in momentum?
A. 0 kg m/sB. 2 kg m/sC. 6 kg m/s
The diagram to the right depicts the before-and after-collision speeds of a carwhich undergoes a head-on-collisionwith a wall. In Case A, the car bouncesoff the wall. In Case B, the car "sticks"to the wall.
1.In which case (A or B) is the change invelocity the greatest?
2.In which case (A or B) is the change inmomentum the greatest?
3.In which case (A or B) is the impulsethe greatest?
4. In which case (A or B) is the force whichacts upon the car the greatest (assumecontact times are the same in bothcases)?
A
A
A
A
The Physics Classroom. [Animations].
Conservation of Momentum
A
B
vA
vB
A
B
vA
vB
B
The total momentum AFTER a collision is equal to the totalmomentum BEFORE.
Types of Collisions:
Elastic Collision – Total Momentum and Kinetic Energy isConserved. Objects do not stick together
The Physics Classroom. [Animations].
Elastic Collision – Total Momentum and KineticEnergy is Conserved. Objects do not sticktogether
The Physics Classroom. [Animations].
2. Perfectly Inelastic Collision – Only Momentum isConserved and the objects stick together.
Types of Collisions:
The Physics Classroom. [Animations].
1.Name the type of collision.
2.What is the momentum of the system beforecollision?
3.What is the final velocity of the system after collision?
Momentum & Impulse - Sample Problems
A 30 kg mass traveling north at 40 m/s collides head on with a 60 kgmass traveling south at 50 m/s. After the collision the 30 kg massmoves south at 50 m/s. What is the velocity of the 60 kg mass after thecollision?
M2
M1
V2f?
Before After
Collision Collision
Your Turn!
A 0.105 kg hockey puck moving at 48 m/s is caught by a 75 kggoalie at rest. With what speed does the goalie slide on theice?
48 m/s
Pause forPractice
Ans: 0.067 m/s
Your Turn!
Determine the post-collision velocity.
(Save for class!)
A 1 kg gun fires a 5 g bullet at a speed of 180 m/s. What is therecoil velocity of the gun?
Save for class!
A 0.112-kg billiard ball moving at 154 cm/s strikes a secondbilliard ball of the same mass moving in the oppositedirection at 46 cm/s. The second billiard ball rebounds andtravels at 72 cm/s after the head-on collision. Determine thepost-collision velocity of the first billiard ball
Bellringer Questions
You have 2 minutes to answer the following questions.
Answer individually!
1.Impulse equals change in momentum.
A. TrueB. False
2. A 500 kg cart is traveling at 10 m/s. What is itsmomentum?
3.Which leads to a greater impulse?
A. A car sticking to a wall
B. A car rebounding off the wall
Collision Videos
Racquet ball
Alciatore, D. High Speed Video Clips
Jello Drop
Alciatore, D. High Speed Video Clips
Water balloon
Alciatore, D. High Speed Video Clips
Soccer Ball Kick
Alciatore, D. High Speed Video Clips
Foot Stomp
Alciatore, D. High Speed Video Clips
Fist Bounding
Alciatore, D. High Speed Video Clips
Rubber ball
Alciatore, D. High Speed Video Clips
Gun Recoil
Alciatore, D. High Speed Video Clips
Water Balloon and Pin
Alciatore, D. High Speed Video Clips
Water Balloon Pop
Alciatore, D. High Speed Video Clips
YouTube.com
Credits:
Alciatore, D.(n.d.). High Speed Video Clips. Colorado State University. Retrieved withpermission from http://high_speed_video.colostate.edu/
Cutnell & Johnson Physics. (2004). [Text Art CD]. John Wiley & Sons.
Foxtrot Cartoon: Bill Amend. Received from 2007 AP Conference ComplimentaryResource CD.
Tippens, P. (2007). Chapter 9A Impulse and Momentum. [PowerPoint Slides]. Receivedfrom 2007 AP Conference Complimentary Resource CD.
The Physics Classroom. [Animations]. http://www.thephysicsclassroom.com