1. Momentum Linear Momentum Impulse Collisions
Physics C Energy
Momentum
11/18/2018
Linear Momentum
Impulse
Collisions
One and Two Dimensional Collisions
Bertrand

2. Physics C Energy
11/18/2018
Linear Momentum
Momentum is a measure of how hard it is to stop or turn a moving object.
p = mv (single particle)
P = Σpi (system of particles)
Bertrand

3. Conservation of Linear Momentum
Physics C Energy
11/18/2018
Conservation of Linear Momentum
The linear momentum of a system is conserved – the total momentum of the system remains constant
Ptot = Σp = p1 + p2 + p3 = constant
p1i + p2i = p1f + p2f
Σpix = Σpfx, Σpiy = Σpfy, Σpiz = Σpfz
“Whenever two or more particles in an isolated system interact, the total momentum of the system remains constant.”
Bertrand

4. Physics C Energy
11/18/2018
Practice Problem 1:
How fast must an electron move to have the same momentum as a proton moving at 300 m/s?
mp= x kg
me= x kg
ve= x 105 m/s
Bertrand

5. Physics C Energy
11/18/2018
Practice Problem 2:
A 90-kg tackle runs north at 5.0 m/s and a 75-kg quarterback runs east at 8.0 m/s. What is the momentum of the system of football players?
ptot= ° N of E
Bertrand

6. Impulse An impulse is described as a change in momentum: I = Dp
Physics C Energy
11/18/2018
Impulse
An impulse is described as a change in momentum:
I = Dp
Impulse is also the integral of force over a period of time:
I =  Fdt or I = FDt
The change in momentum of a particle is equal to the impulse acting on it
Bertrand

7. F=ma!!! Practice Problem 3:
Physics C Energy
11/18/2018
Practice Problem 3:
Show that Impulse actually comes from Newton’s 2nd Law
F=ma!!!
F = ma = m (Δv/Δt)
m(Δv) = FΔt
Δp = FΔt
Bertrand

8. Impulsive forces are generally of high magnitude and short duration.
Physics C Energy
11/18/2018
Impulsive forces are generally of high magnitude and short duration.
time
Force
Bertrand

9. ptot= 2.12 kgm/s @ 62.8° above -x
Physics C Energy
11/18/2018
Practice Problem 4:
A 150-g baseball moving at 40 m/s 15o below the horizontal is struck by a bat. It leaves the bat at 55 m/s 35o above the horizontal. What is the impulse exerted by the bat on the ball?
If the collision took 2.3 ms, what was the average force?
ptot= ° above -x
Bertrand

10. Physics C Energy
11/18/2018
Practice Problem 5:
An 85-kg lumberjack stands at one end of a floating 400-kg log that is at rest relative to the shore of a lake. If the lumberjack jogs to the other end of the log at 2.5 m/s relative to the shore, what happens to the log while he is moving?
The log will move at .53 m/s in the opposite direction of the lumberjack
Bertrand

11. Physics C Energy
11/18/2018
Practice Problem 6:
Two blocks of mass 0.5 kg and 1.5 kg are placed on a horizontal, frictionless surface. A light spring is compressed between them. A cord initially holding the blocks together is burned; after this, the block of mass 1.5 kg moves to the right with a speed of 2.0 m/s.
What is the speed and direction of the other block?
What was the original elastic energy in the spring?
a) v2f= -6 m/s
b) Us = 4.5 J
Bertrand

12. Practice Problem 7: (1-D conservation of momentum)
Physics C Energy
11/18/2018
Practice Problem 7: (1-D conservation of momentum)
What is the recoil velocity of a 120-kg cannon that fires a 30-kg cannonball at 320 m/s?
Vcf = -80 m/s
Bertrand

13. Physics C Energy Elastic Inelastic Perfectly Inelastic
11/18/2018
Collisions
Elastic
Inelastic
Perfectly Inelastic
Bertrand

14. Collisions: In all collisions, momentum is conserved.
Physics C Energy
11/18/2018
Collisions:
In all collisions, momentum is conserved.
Elastic Collisions: No deformation occurs
Kinetic energy is also conserved
Inelastic Collisions: Deformation occurs
Kinetic energy is lost
Perfectly Inelastic Collisions
Objects stick together, kinetic energy is lost
Explosions
Reverse of perfectly inelastic collision, kinetic energy is gained
Bertrand

15. Elastic Collisions Objects collide and return to their original shape
Kinetic energy remains the same after the collision
Perfectly elastic collisions satisfy both conservation laws shown below
Billiard balls colliding are nearly perfectly elastic. Ideal gases undergo perfectly elastic collisions between molecules and between the walls of the container.

16. Inelastic Collisions Momentum is Conserved:
m1iv1i +m2iv2i = m1fv1f +m2fv2f
Kinetic energy is less after the collision
It is converted into other forms of energy
Internal energy - the temperature is increased
Sound energy - the air is forced to vibrate
Some kinetic energy may remain after the collision, or it may all be lost
If the objects are still moving after the collision, then there is still some KE. If both objects have stopped, such as might occur in some head-on collisions, then all of the KE is converted into other forms of energy.

17. Perfectly Inelastic Collisions
Two objects collide and stick together
Two football players
A meteorite striking the earth
Momentum is conserved
Masses combine
Ask students to suggest additional examples of perfectly inelastic collisions.

18. Practice Problem 8: (1-D elastic collision)
Physics C Energy
11/18/2018
Practice Problem 8: (1-D elastic collision)
A proton, moving with a velocity of vi, collides elastically with another proton initially at rest. If the two protons have equal speeds after the collision, find
the speed of each in terms of vi and ...
the direction of the velocity of each
vf = ½ v1i
This plot illustrates the tremendous complexity of the proton-Proton collisions that occur at the Large Hadron Collider.
Bertrand

19. Practice Problem 9: (1-D perfectly inelastic collision)
Physics C Energy
11/18/2018
Practice Problem 9: (1-D perfectly inelastic collision)
A 1.5 kg cart traveling at 1.5 m/s collides with a stationary 0.5 kg cart and sticks to it. At what speed are the carts moving after the collision?
Vf = m/s
m1 = 1.5 kg
V1i = 1.5 m/s
m2 = .5 kg
V2i = 0 m/s
Bertrand

20. Practice Problem 10: (1-D elastic collision)
Physics C Energy
11/18/2018
Practice Problem 10: (1-D elastic collision)
A 1.5 kg cart traveling at 1.5 m/s collides elastically with a stationary 0.5 kg cart. At what speed are each of the carts moving after the collision?
V1f = .75 m/s
V2f = 2.25 m/s
m1 = 1.5 kg
V1i = 1.5 m/s
m2 = .5 kg
V2i = 0 m/s
Bertrand

21. Physics C Energy
11/18/2018
2-D collisions
Use conservation of momentum independently for x and y dimensions
You must resolve your momentum vectors into x and y components when working the problem:
m1v1ix + m2v2ix = m1v1fx + m2v2fx
m1v1iy + m2v2iy = m1v1fy + m2v2fy
Bertrand

22. Practice Problem 11: (2-D collision)
Physics C Energy
11/18/2018
Practice Problem 11: (2-D collision)
A pool player hits a cue ball in the x-direction at 0.80 m/s. The cue ball knocks into the 8-ball, which moves at a speed of 0.30 m/s at an angle of 35o angle above the x-axis.
Determine the velocity and angle of deflection of the cue ball.
(assume m1 = m2)
V1f = ° below -x
Bertrand