![Page 1: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/1.jpg)
Chapter 6Momentum and Collisions
![Page 2: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/2.jpg)
…What Would You Rather Be Hit With!!!!
Today’s Choices Are……Mr. Friel’s Dry Erase Marker!!!…Mr. Friel’s Whiffle Ball !!!…Mr. Friel’s 10.00 kg shot put!!!
Now Choose!!!!!
Let’s Play…
![Page 3: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/3.jpg)
Why did you make your decision?
Now…the Bonus Round!!!
Who would you rather have throw the object?…Mr. Frielor…Aroldis Chapman, 105 mph flamethrower for the Cincinnati Reds
![Page 4: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/4.jpg)
What factors were involved in your decision?- mass- velocity
Remember, Fnet = ma = m (Δv/Δt)
- it takes force to alter the motion of an object
Ex.Randy Johnson Pitch
![Page 5: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/5.jpg)
Momentum (p) – possessed by any object in motion (must have mass and velocity)
p = mv
- SI Units are kg m / s
- Vector quantity, the direction of the momentum is the same as the velocity
The amount of momentum is also directly proportional to the inertia when an object is moving.
![Page 6: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/6.jpg)
As long as no external force (friction) acts on an object in motion, momentum is conserved (Δp = 0)
Any change in momentum due to an outside force is known as impulse.
Conservation of Momentum and Impulse
![Page 7: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/7.jpg)
F = maF = m (Δv/Δt), multiply both sides by Δt Impulse = FΔt = mΔv = Δp
Vector quantity, the direction is the same as the direction of the force.
Impulse
![Page 8: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/8.jpg)
The theorem states that the impulse acting on the object is equal to the change in momentum of the object.
◦ ◦ If the force is not constant, use the average force
applied
Impulse-Momentum Theorem
fit m mI F p v v
![Page 9: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/9.jpg)
Think about how an airbag works in a car- increases Δt- decreases ΔF
What if you hit the steering wheel?- ouch…
What are some other objects that take advantage of impulse?
Why can we belly flop onto our beds, but not onto the kitchen floor, and other pertinent questions of our time…
![Page 10: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/10.jpg)
Let’s do another quick example, everyone climb up onto your chair……now jump off……how did you land?
…what happed to your knees?
![Page 11: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/11.jpg)
Conservation of Momentum, Example
The momentum of each object will change
The total momentum of the system remains constant
![Page 12: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/12.jpg)
When objects collide, total momentum change (impulse) = 0
Initial momentum (pB + pA) is equal to final momentum (pB’ + pA’)
Notice how Δp for object A and Δp for object B are exact opposites.
ΔpA = - ΔpB
![Page 13: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/13.jpg)
Law of conservation of momentum – the momentum of any closed, isolated system does not change
- no net external forces
![Page 14: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/14.jpg)
Mathematically:
◦ Momentum is always conserved for the system of objects
◦ p1init + p2init = p1final + p2final
Conservation of Momentum
1 1 2 2 1 1 2 2i i ffm m m m v v v v
![Page 15: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/15.jpg)
Momentum is conserved in any type of collision
Collisions are one of the following:
◦ Perfectly elastic
◦ Perfectly inelastic
◦ Somewhat elastic
Types of Collisions
![Page 16: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/16.jpg)
Only happens in a closed system (no friction in collision, no thermal energy loss).
Both momentum and kinetic energy conserved in a perfectly elastic collision.
Perfectly Elastic Collisions
![Page 17: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/17.jpg)
Inelastic collisions◦ Kinetic energy is not conserved◦ Perfectly inelastic collisions occur when the
objects stick together Not all of the KE is necessarily lost In a perfectly inelastic collision, the final velocity is
the same for both objects
Example of Perfectly Inelastic Collision - Office Linebacker
Perfectly Inelastic Collisions
![Page 18: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/18.jpg)
More About Perfectly Inelastic Collisions
When two objects stick together after the collision, they have undergone a perfectly inelastic collision
Conservation of momentum becomes
◦ Because the masses have stuck together after colliding and are moving at the same velocity
f21i22i11 v)mm(vmvm
![Page 19: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/19.jpg)
Perfectly elastic collision◦ Both momentum and kinetic energy are
conserved
Actual collisions◦ Most collisions fall between perfectly elastic and
perfectly inelastic collisions◦ In this case, kinetic energy is not conserved
either.
More Types of Collisions
![Page 20: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/20.jpg)
Both momentum and kinetic energy are conserved
Typically solved using systems of equations – two equations, two unknowns
More About Elastic Collisions
2f22
2f11
2i22
2i11
f22f11i22i11
vm2
1vm
2
1vm
2
1vm
2
1
vmvmvmvm
![Page 21: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/21.jpg)
For a collision of two objects in three-dimensional space, the conservation of momentum principle implies that the total momentum of the system in each direction is conserved
Glancing Collisions
fy22fy11iy22iy11
fx22fx11ix22ix11
vmvmvmvm
andvmvmvmvm
![Page 22: Momentum and Collisions. …What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649f2f5503460f94c49268/html5/thumbnails/22.jpg)
Glancing Collisions
The “after” velocities have x and y components Momentum is conserved in the x direction and in the y
direction Apply conservation of momentum separately to each
direction