# Momentum and Impluse

1) Suppose you catch a baseball and then someone invites you to catch a bowling ball with either the same momentum or the same kinetic energy as the baseball, which would you choose?

(I think kinetic energy because the total work required to stop the baseball is 1/2mv^2 and its pretty easy to catch a base ball...ie doesnt require much work) I'm not really understanding the concept of momentum so I could be very wrong.

2) When rain falls from the sky, what happens to its momentum? Is your answer valid with newtons famous apple?

(I think since P = mv that the velocity goes to zero when it hits so momentum must go to zero, and I think this must also hold true for newtons famous apple)

3)When a large heavy truck colides with a small passenger car, the people in the car are more likely to be injured than the driver of the truck, why is this?

(I dont know how to explain this one, I dont really understand the concept of momentum so I dont know how to explain it, this question says nothing about mass or velocities of the car & truck, i dont know what to say about this)

Brian
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Commented:
1) the same momentum
2) yes, it goes to zero when it hits.  having transfered it to the ground (is that what the question is asking?)
3) the people in the small car, other things being equal

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Commented:
momentum is propotional to mv while kinetic energy is proporional to mv²
so if the mass of a bowling ball is 49 times the mass of a baseball
a bowling ball with the same kinetic energy as the baseball will have 7 times as much momentum
while a bowling ball with the same momentum as the baseball will have 1/7th as much kinetic energy as the baseball
Author Commented:
Hey Ozo,

I kinda understand that much p = mv, k = 1/2mv^2, what I dont understand is the physical effects.. For example in problem 1, if momentum is the same shouldnt it be just as easy to catch if the kinetic energy is the same? I know by the work energy theorem that W = k2 - k1, so W = -k1, so it would make sense to say since the same ammount of work is require to stop the bowling ball, we should chose kinetic energy...

I really dont understand this stuff all that well.

Brian
Commented:
A bowling ball with the same momentum as a baseball will be moving slower
than a bowing ball with the same kinetic energy as a baseball
I'd rather catch the bowling ball that is moving slower.
Commented:
momentum = mass * velocity
baseball 1 kg*10 meters/sec = bowling ball 10 kg* 1meter/sec

kinetic energy = 0.5*mass*velocity^2
baseball 0.5*1kg*10^2 = bowling ball 0.5*10kg* 3.1623^2

1. Bowling ball, its bigger so more surface contact area, which probably means that it won't sting as much if momentum is equal.

2. I think terminal velocity is 98meter/s.  At some point when an object is falling; the co-efficient of resistance in air stops acceleration, so eventually you get a constant velocity.  I am not sure about it being 98m/s though.

rain momentum is mass of water droplet * terminal velocity.

3. truck has greater momentum than car going at the same speed.  Net force on a truck is still postive when it hits a car going at the same speed coming towards it.  Car during impact will have a negative net force applied to it.

I'm not sure but the passengers in the car may be experiencing a sheering force on impact.  Imagine the difference between a quick decceleration and a negative vector change.

Regards,
Commented:
98meter/s = 352.8 kilometre/hour
Catching bowling balls is probably safer than than going out in that kind of rain.

A heavy vehicle would experience less velocity change than a light vehicle when they exchange momentum.
Author Commented:
>>A bowling ball with the same momentum as a baseball will be moving slower
>>than a bowing ball with the same kinetic energy as a baseball
>>I'd rather catch the bowling ball that is moving slower.

How do you determine this?

I understand why a bowling ball will be moving slower if it has the same momentum.

How did you determine that with the same kinetic energy the bowling ball would be moving faster?
Commented:
a 143 gram baseball moving at 24.5m/s has the same kinetic energy as a 7007gram bowling ball moving at 3.5m/s
7007gram(3.5m/s)²/2 = 143 gram(24.5m/s)²/2
a 143 gram baseball moving at 24.5m/s has the same momentum as a 7007gram bowling ball moving at .5m/s
7007gram(.5m/s) = 143 gram(24.5m/s)

Commented:
I'll catch the rain that falls, anyone else can catch the bowling balls.  lol
Like I said, I wasn't entirely sure about that number.  and again air resistance does come into play.  Think about rain, hail storms and meteors.

to determine V for the, you isolate V for the bowling ball or baseball.
Let L=baseball
Let B=bowlingball

The relationship becomes
Momentum(L)=Momentum(B)

subsituting the equation
Velocity(L)*Mass(L)=Velocity(B)*Mass(B)

to determine Velocity(B) divide by Mass(B)
Velocity(B)= (Velocity(L)*Mass(L))/Mass(B)

to determine Velocity(B) for the kinetic energy

the relationship is
0.5*mass(L)*(velocity(L))^2=0.5*mass(B)*(velocity(B))^2

when you divide and sqrt out everything on the B side, you get

velocity(B) = sqrt((mass(L)*(velocity(L))^2)/ mass(B))

Regards,

Commented:
1.
Let the baseball's velocity be v1 and mass be m.
K.E. of baseball = 1/2 m * v1^2
momentum = m * v1

Let the bowling ball be k times more massive than the baseball.
K.E. of bowling ball = 1/2 k * m * v2^2
momentum = k * m * v3

When the kinetic energies are the same, v2 = sqrt(1/(2k)) * v1
When the momenta are the same, v3 = 1/k * v1

I assume you want the bowling ball to be going as slowly as possible.
So which is smaller?  When k < 2, v2 will be smaller.  When k > 2, v3 will be smaller.  Using real world knowledge, we know k is much greater than 2, so we want the momenta to be the same.

2.  See http://en.wikipedia.org/wiki/Terminal_velocity.  Apples falling from trees don't typically reach terminal velocity (if it were next to a cliff, however...)

3.  Assuming here that the question isn't about crushing effects, etc.  The differential velocity of the truck before and after the collision will be much smaller than that of the car.  Injuries caused by sudden acceleration/deceleration (not engine/brakes, but running-into-a-brick-wall type decelration) will be much more severe in the car.
Commented:
When k < 1, v2 will be smaller.  When k > 1, v3 will be smaller.
Commented:
the expressions in question are (if I'm not mistaken) sqrt(1/(2k)) and 1/k.

When k = 2, sqrt(1/(2*2)) = 1/2.
Commented:
When k = 1, the bowling ball and the baseball will have the same speed.
Commented:
2) When rain falls from the sky, where do the momentum go?
it pushes the rest of the earth down, but not very much since drops don't weigh much
3) why do car occupants get hurt?
cars are made MUCH less sturdy than trucks, so that the same amount of whack does not result in the same amount of squich.   The car crumples into the people; that is what hurts them, not the bump itself.
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