Physics Question
 

I have recently become fascinated with physics. As in the last hour.

Here is the question:

10lb object in space moving at 10mph hits 5lb object moving Zerio Mph. The collision is dead on. What is the resulting speed of each object?

I know that the kinetic energy of the original object was 500 initially. But I don't know how much transfers to the stationary object.

Whats weird is that I have a known fact- if the object was to hit another object of equal weight, the original object would stop completely and the 2nd object would take on all of the original speed. Like in curling if you were to hit the other rock dead on, or those desktop thingies where you have 5 balls, drop one and the one on the other side goes up equally, then back and forth indefinitely (until friction with the air and the collision heat and sound eventually stops it)

Assume zero friction, meaning no loss of kinetic energy due to heat loss or sound waves.

Pi.

Oh yes please. I missed lunch.

Try asking in here:
http://www.physicsforums.com/

assuming a completely elastic collision (like steel ball striking steel ball, not steel ball striking marshmallow fluff) I think we're dealing with conservation of momentum.

p=mv, and in a closed system, it's a constant. unlike kinetic energy.

v_{1,f} = \left( \frac{m_1 - m_2}{m_1 + m_2} \right) v_{1,i} + \left( \frac{2 m_2}{m_1 + m_2} \right) v_{2,i} \,

v_{2,f} = \left( \frac{2 m_1}{m_1 + m_2} \right) v_{1,i} + \left( \frac{m_2 - m_1}{m_1 + m_2} \right) v_{2,i} \,

I don't think that's going to read very well, so check out here: http://en.wikipedia.org/wiki/Momentum

What's going to be the interest in the next hour? :D

JP

0 mph for the 10-lb object: contingent on its insurance policy being canceled.

Nope- I thought this at one point, but it fails like this:

Initial system Energy MUST EQUAL New System Energy

Initial system Energy = 500

In your new system, its (10)(5 squared) + (5)(10 squared) = 750

You've created energy.

I've been research elastic collisions... and yes, we are talking like two steel balls, no marshmellows. I am looking at the page you linked, and much like I always felt in school, its too much to take in- could you plug my numbers into a formula? Please? You know you want to show just how smart you are...

That is the full formula..

The best cheat sheet I can figure:

With one object half as heavy as the other, the heavy object slows to 1/3 the orginal speed and the lighter one accelerates to 4 times that slower speed.

Try that out (rounding up or down a sukosh..) and see if it works..

In a closed system, a 100% elastic collision conserves both momentum and kinetic energy

In a closed system, a 100% inelastic collision only conserves momentum.

This thread is hilarious.

CONSERVATION OF FOUR-MOMENTUM, USE IT!

Smaller object now traveling at 20mph. Larger object not moving.

JR

that got me thinking... did you guys & gals in the US have to learn Physics using Imperial Units?

I learned kilograms, m/s, f/s, slugs (the mass version of pounds which is force, not mass), pounds, Newtons, etc... I couldn't tell you diddley about "stones", but I've got what the US calls Standard/English and metric down.

Most of our word problems and work was done in metric units.

IIRC, it should be 1/3 of V1 for M1 and 4/3 of V1 for M2. So 3.3333mph and 13.3333mph.

i refuse to look it up, but that exact problem (diff masses i am sure) is in my dynamics textbook. it is rather simple, from what i remember. which is almost zero. heheh.

Does the 10-pound object have a "Type R" sticker on it? If so, you can't ignore it's massive torque.

Pool. Lots of Pool. Then add spin......

Sometimes, the hardest questions are best answered while on the crapper.

After the collision, the 5lb object will be moving at the speed of 4 Libraries of Congress.

LOL!!

KE=1/2 M*V^2, Inelastic collisions. Energy must be conserved. Figure it out.

Think billiard balls, no english.

Ball that is not moving has 0 KE as V=0

Energy is conserved, therefore all KE is transfered to 2nd ball leaving the initial ball with 0 KE, ie no longer moving.

The velocity of the lighter ball will be = 1.41 x the velocity of the heavy ball (the sqrt of 2 more precisely)

Want to check it out. Figure the KE of the 20 pound ball, then assume a velocity of 1.41 times that velocity for the 10 pound ball. The KE's are equal. Energy is conserved. QED

Now for a difficult question. Why do you launder a wash cloth? ITs clean, you use soap and water to use it. Why doesn't the soap and water clean the wash cloth? Just wondering.

Then theres the towel. Its clean, your clean, just water on you. You wipe down. Yet you still have to launder it!! WHY?

I am sitting here, waiting to wipe my butt, just wondering, just wondering.

I'll use caps for mass and Velocity, so the subscripts, i and f for initial and final and 1 and 2 for the two objects make more sense.

M1V1i + M2V2i = M1V1f + M2V2f
and
1/2 M1V1i^2 + 1/2 M2V2i^2 = 1/2 M1V1f^2 + 1/2 M2V2f^2

What it all comes down to is
V1i + V1f = V2i + V2f or
V1i - V2i = -(V1f - V2f)

excerpt from my college physics book concerning elastic collisions.
Physics for Scientists & Engineers 2nd ed, Serway
Eq 9.22 says that V1f equals the difference of the masses divided by the sum of the masses times the initial velocity of that particle.

so V1f = 5/15 * 10 or 3.333mph

Eq 9.23 says that V2f equals double the mass of particle 1 divided by the sum of the masses times particle 1's initial velocity.

so V2f = 20/15 * 10 or 13.333mph

Based on the math in the first two equations, I get different answers. I'm guessing that the difference between 10# and 5# is not enough to use the second set of equations.

Here are the results with the first set of equations. The one thing that seems odd to me is the final speed of the second particle. I'd expect it to be higher.
10*10 + 5*0 = 10*V1f + 5*V2f
.5*10*10^2 + .5*5*0^2 = .5*10*V1f^2 + .5*5*V2f^2

so
V1f = 10 - .5*V2f -- substituting that into the second equation we get

.5*10*100 + 0 = .5*10*(10 - .5*V2f)^2 + .5*5*V2f^2

when I solve, I get that V2f = 0 or 1.333.... since the weights aren't equal, it's not 0, then plugging 1.333 back into the first equation I get V1f = 9.3333

So part of that seems correct. The speed of the first ball hasn't changed by much since the second ball is lighter. So it only slows from 10 -->9.333..., but I'd expect the second ball to be going faster. So I'm not sure what, if anything I did wrong.
so, after, the 10 ball would be moving at 9.333 and the 5 would be going 1.333

Maybe I got the answers backwards. Maybe the masses are close enough that the first ball almost stops and the second ball is going almost as fast as the first.

Only problem here is that the heavy particle is NOT much larger than the light particle. Much heavier imply s a factor of at least 10. In your case likely a factor of 1000 or more. Also the collision is not totally inelastic in your case, because energy MUST be conserved. The lighter ball MUST end up going faster than the heavy ball. Your calcs are probably what a real item would do (elastic}, but we are dealing with ideal (inelastic) balls here.

Anyone can do the math, its the setup that separates the men from the boys.

For this to work, the balls have to be the same size, like pool balls, even though the weights are different.

So the contact is square on.

I thought the balls were in space?? But yes, they have to hit square..

A few things here-

#1- I just got back to this thread, so I am going to try out the math and make it work.

#2- Yes, in my scenario, the objects are hitting perfectly square.

#3- An answer to the question about washing towels. In college, I decided to not wash my towels for this very reason- I was clean from the shower, so what would the point be in washing the towel? This proved to be fine for awhile. But about 2 months in, the towels start to have an odor, and it eventually gets pretty foul. They do in fact get dirty, and its from dead skin cells, slow growing mold, and little amounts of dirt that you miss when you shower. Washing towels after every use is stupid, but once a week or so is reasonable. Never washing them makes them smell bad. I know this for a fact.

Exactly on the towels. You put the towels up wet, they are in the bathroom with the shower, so the environment is probably warm and humid, and then when you leave, it's probably dark. Even without the dead skin, the things are dark, warm and wet which is ideal for mold/mildew.

Want to test the worst case scenario. Wash a load of laundry, but leave it in the washing machine for several days without drying the wet stuff. It'll smell horrible, and it's just been washed, hell, it's still sitting in the washing machine.

You take off to a distant planet at twice the speed of light, you land, get out and set up a telescope, can you see yourself coming?

My cat's name is Mittens.

http://forums.pelicanparts.com/uploa...1196458004.jpg

This is my all time favorite answer to a physics question that I wish I used back in school:

http://i11.tinypic.com/40nxf83.jpg

How much is a Zerio?
:D

If lesbian #1 is traveling at 10 Mph and hits lesbian #2 who is traveling in the same direction at 15 Mph what speed are lesbian #1 and #2 traveling after the collision?

You're ignoring the effects of gravitational attraction between the two masses.

Also relativity and some ***** to do with quarks. And elves.

The equations that I used were correct and were setup correctly. I just did the math wrong. I guess that's what I get for working on this when I was tired.

When I re-did the math I got the same thing that Steve/sjf911 got in his simple, short post
My equations were for an elastic collision and did take conservation of energy and momentum into account.

before collision -- mv + mv = mv + mv -- after collision -- momentum
and
before collision -- 1/2 mv^2 + 1/2 mv^2 = 1/2 mv^2 + 1/2 mv^2 -- after collision -- KE

so, the big ball would be going 3.333 mph after the collision and the small ball would be going 13.333 mph after the collision. Not really quite double the speed of the big one.

I don't think so.