Physics 101: Lecture 12, Pg 1 Physics 101: Lecture 12 2D Collisions and Center of mass

Physics 101: Lecture 12, Pg 1

Physics 101: Physics 101: Lecture 12Lecture 122D2D Collisions and Collisions and

Center of massCenter of mass


Example: stopping carExample: stopping carVo=40 m/s

m = 1500 kg

µs = 0.6

How long does it take the car to stop?


Momentum is ConservedMomentum is Conserved

Momentum is “Conserved” meaning it can not be created nor destroyed Can be transferred

Total Momentum does not change with time.

This is a BIG deal!

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Example: collisionExample: collision“before” “after”

M1=2kg M2=3kg M2=3kgM1=2kg

Vo = 5m/sVo = 0m/s

Two blocks collide and stick together, what is their final velocity?




Vo = 5m/sVo = 2m/s

Two blocks collide and stick together, What direction is their final velocity?

A)Right

B)Left

C)The final velocity is zero




Vo = 5m/sVo = 2m/s

Two blocks collide and stick together, what is their final velocity?


Example: cannon (explosion)Example: cannon (explosion)

mc = 200kgmb = 5 kg

v = 300 m/s

What is the velocity of the cannon?



ExplosionsExplosions “before”

“after”

M

m1m2

• Example: m1 = M/3 m2 = 2M/3• Which block has larger |momentum|?

* Each has same |momentum|

• Which block has larger speed?

* mv same for each smaller mass has larger velocity

• Which block has larger kinetic energy?

* KE = mv2/2 = m2v2/2m = p2/2m

* smaller mass has larger KE

• Is mechanical (kinetic) energy conserved?

* NO!!

v1 v2

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A=1, B=2, C=same

0 = p1+p2

p1= -p2


Collisions or Explosions in Collisions or Explosions in Two DimensionsTwo Dimensionsy

x

before after

• Ptotal,x and Ptotal,y independently conserved

Ptotal,x,before = Ptotal,x,after

Ptotal,y,before = Ptotal,y,after37


before afterppf

vvoo = 3m/s = 3m/s

FF

vvcm

Example: shooting poolExample: shooting pool

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during

Mass of both balls is 2kg

300

Find final velocity and direction of white ball

At rest

vvf =2m/s

vvf =2m/s


Example: shooting pool (cont.)Example: shooting pool (cont.)


Block 1 of mass M1 = 10kg has an initial velocity of 5m/s in the Block 1 of mass M1 = 10kg has an initial velocity of 5m/s in the +x direction. It collides with Block 2 of mass M2 = 5kg which, +x direction. It collides with Block 2 of mass M2 = 5kg which, initially has a velocity of 15m/s in the +y direction. If the two initially has a velocity of 15m/s in the +y direction. If the two

blocks stick together what is the final speed and direction of the blocks stick together what is the final speed and direction of the two blocks?two blocks?


H

L LL L

m

M

A projectile of mass m moving horizontally with speed v strikes a stationary mass M suspended by strings of length L. Subsequently, m + M rise to a height of H.

Given H, M and m what is the initial speed v of the projectile?

M + mv

V

V=0

See I.E. 1 in homeworkSee I.E. 1 in homework

Ballistic PendulumBallistic Pendulum

demo 29


Ballistic PendulumBallistic Pendulum

Collision Conserves Momentum

After, Conserve Energy

Combine:


Center of MassCenter of MassCenter of Mass = Balance point

i

cm m

rmrmr 2211

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Some objects can’t be balanced on a single point


Example: center of massExample: center of mass

m = 0.140 kg

1m

0.1m

M =

0.515


SummarySummary• Collisions and Explosions

•Draw “before”, “after” •Define system so that Fext = 0

•Set up axes•Compute Ptotal “before”

•Compute Ptotal “after”

•Set them equal to each other

• Center of Mass (Balance Point)

icm m

rmrmr 2211

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Physics 101: Lecture 12, Pg 1 Physics 101: Lecture 12 2D Collisions and Center of mass