TAKE HOME QUIZ What is the difference between momemtum and kinetic energy ?

Let's try to understand the difference between these 2 physical quantities.
First note that momentum (p = mV)  is a _________ because it has a direction and a magnitude.
kinetic energy (0.5 mV²) is a ______________. (no direction)
A) Consider the situation where you have 2 wagons, with the same mass m. The first wagon is moving toward a second wagon at rest.
They both  have the same mass m. After the collision, they stick together and move with a speed V'. (see worksheet momentum).


A) Let's look at the conservation of momentum again. We neglect friction. Let's say the wagon 1 moves at a speed V before collision.
The conservation of momentum tells us that after the collision, the wreck moves at a speed of V' = ____________.
hint: write the algebraic expression. use only V ,the variables  m cancel out. An algebraic expression is an expression with variables and operations
like 2x / y² is an algebraic expression
So the first wagon walloped the second one and shared its momentum with it.

B) now let's look to what happened to the kinetic energy.
before collision, total kinetic energy = kinetic energy of wagon 1 = _________ (algebraic expression with variables m and V)
after collision, total kinetic energy = kinetic energy of the wreck  = __________
hint: mass of wreck is  2m and speed of wreck is  V'=V/2 see A) - The algebraic expression has only m and V. simplify the expression.

So the kinetic energy is not conserved. kinetic energy after collision = ____ kinetic energy before collision. (hint: is it twice ? half ? third ? fourth ?)
What do you think happened to this missing energy ? ____________________________________________-
So kinetic energy is the ability to cause damage, to apply a force through a distance. (the wagon will damage the second one by going into it)
momentum is the ability to wallop, to knock over.

C) Let's take another example. Imagine 2 football players, moving toward each other, with the same speed V. They have the same mass m.
The first player run @ right so p1 = mV   , the second player run @ left toward the first one so p2 = - mV   (same speed, same mass)
before collision the total momentum is p1+ p2 =  _________ (use you algebra skills, collecting like terms)

since momentum is conserved (we neglect outside forces), the total momentum after is still  _________. (same as before)
The collision is not elastic. (they don't bounce off, not a hit and bounce situation). So the only way to get the same momentum after is that
after the collision, the 2 payers just s__________ moving. Their speed after the collision is ___________.

let's look at the kinetic energy. before the total kinetic energy = ______________
(hint; use your algebra skills, add kinetic energy player 1 + kinetic energy player 2. collect like terms, use the variables V and m)
But the total kinetic energy after = ___________. (are they moving ?  ).
where did the kinetic energy go ? __________________________________________________________________--
So momentum was used to stop the payer from moving (change the motion, they wallop, knock over each other)
 but the kinetic energy caused ____________________. The kinetic energy went into bruises and maybe broken bones.

D)  Imagine 2 football players. a small one with mass m and a heavy one with mass 2m (twice as heavy as the other guy).
The heavy one run with a speed V and the small one with a speed 2V (twice as fast).
you are given the choice to be knocked over by the small but fast guy or by the heavy but slow guy/
predict first and then we will check your prediction.
Which one with cause more damage to you ? _______________ Will both players they cause the same change in your motion? _______________
(that is will you be knocked over the same way ? same change in motion ? )

Let's compare their momentum;
small and fast guy p1 = ___________. (algebraic expression, speed is 2V and mass is m) 
big and slow guy p2 = ______________. (mass is  2m and speed is V)
Do they have the same momentum ? ___________ Will they knock you over the same way ____________ ?
Will they produce the same change in motion ? ______  (same change in speed and direction that is same change in velocity)

Let's compare their kinetic energy.
small and fast guy KE1 = ____________ (algebraic expression, mass is m speed is 2V. simplify) .
Heavy and slow guy KE2 = ___________ (algebraic expression, mass is 2m and speed is V. simplify)
Compare the kinetic energy KE1 and KE2. Is it the same  ? KE1 is ___________ KE2.  (same? greater ? smaller? )
So which one will cause you more bruises and broken bones ? _____________________________
( you break bones, you cause bruise by applying a force over a  _____________ )

E) Consider a plastic bullet knocking over a block. see second picture below. (from Paul Hewitt, conceptual Physics)

The bullet is moving at a speed V toward the block and bounces back at the same speed. The impulse knocks the block over.
the mass of the bullet is m and the mass of the block is M.
before collision the momentum of the bullet is p1 = _______ (use m and V, algebraic expression). The momentum of the block is p2= _____. (not moving)
The momentum of the ball after the collision is p1' = __________. (same speed V but opposite direction, use a negative sign for @ left).
So the change in momentum ∆p1 = p1' - p1 for the bullet is _________ (algebraic expression, collect like terms, remember - (-) is + use m and V ).
This change in momentum produces an impulse that knocks over the block. (wallops the block).

Suppose the big block has a mass M (big compared to m) and a velocity V'.
The change in momentum of the big block is ∆p2 = p2' - p2 = p2' =_________  (with p2 = 0, mass  M and velocity V')
Using the conservation of momentum : ∆p1 =- ∆p2     (momentum lost by 1 = momentum gained by 2)
Find the speed of the block V' .  V' = ____________.
(hint: solve for the variable V' in the expression 2mV = M V' )
However, M is really  big compared to m, m/M is really small so V'  is almost ______ . The big block is not moving very far.
So, the block hardly moved, just enough to be knocked over.

Now the total kinetic energy before collision = kinetic energy of the bullet =  _________ (use m and V, the big block is not moving)
The total kinetic energy after collision = kinetic energy of bullet =  ______________
 (hint: use m and V, if V' is small, V'² is really small so forget about the kinetic energy of the block).
So although the block is knocked over, there is no _____________done because no change in kinetic energy.
Why do you think policemen use rubber bullets? _________________________________________________________
_________________________________________________________________________________________________

F) When the bullet does not bounce off the block (real bullet) but goes inside, you get the same situation as for the 2 wagons colliding.
The change in momentum of the bullet cause the block to change its ___________ but the kinetic

                            
conclusion:
So kinetic energy is the ability to cause __________, to apply a _____________ through a distance. (the wagon will damage the second one by going into it,
or the football player will go into the other or the bullet will go into the block). momentum is the ability to _________, to__________over.

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