Question

in an elastic collision between a moving object and a stationary object. is it always true that the obj on the left can only bounce back or stop? (1d motion) why can't it also move in the positive direction too

Answer 1

it can


imagine a rock going and colliding with a pebble, will the rock reverse its directino?!

Answer 2

that may not be elastic

Answer 3

because when i do it mathematically, i don't get a value

Answer 4

elastic or not depends on material..
you can always make it elastic by choosing the right material

(maybe a super elastic basket ball, and a small tennis ball?)

Answer 5

you do.. what is your math expression?

Answer 6

Clarifying the prompt will help a little: Is the object on the left the one that is stationary, or the one on the right? I'm guessing the one on the right is stationary and the one on the left is moving towards it.

I know how we can show specific cases, but I'm certain there's a way we can mathematically show it to be true as a general case as well.

Answer 7

yes its the object on the right thats stationary

Answer 8

Oh, and is it the special case where both masses are equal, or is there a significant difference between the masses?

Answer 9

the masses aren't equal

Answer 10

i also recall the professor saying that in an elastic collision, if the second obj is stationary, the left obj will either bounce back or stop. but i don't understand why

Answer 11

@physo

No it won't.. either what your professor said is wrong, or maybe you mis heard him or something..

Answer 12

can you give me an example with values?

Answer 13

https://www.youtube.com/watch?v=SUYnS7rj33w

plz look at this lecture...
i guarantee you, all your doubts will be cleared.. its a personal 100 percent guarantee i can give :) :) :) :P

Answer 14

you probably just have to watch the first 15 or 20 mins.. thats it!

Answer 15

What? Yes, the left object will stay still or possibly bounce back a little in a perfectly elastic collision dependent on the mass, Physo's professor is right. If a mass collides with an identical, still mass, the first mass in an elastic collision will stop, and the second one will move;

When masses are unequal and there are *significant* differences between the mass, you can make generalizations about the final velocity of one of the objects.

Answer 16

I can at the very least show the case for where a very large object collides with a very small object, one moment.

Answer 17

@Mendicant_Bias

IF the stationary object is LESS massive (doesn't matter how much).. than the moving object, after collision they end up travelling in the same direction!

Answer 18

so that answers the original question.. "can the moving object continue in its direction after collision??
YES it can.. provided its more massive than the stationary object.

Answer 19

i don't think that proves anything

Answer 20

@physo ??
tat was your original question.. right?!
you want proof?
watch the lecture..

Answer 21

so i used the equation in the lecture

Answer 22

ok.. and?

Answer 23

is there a way i can attach a photo

Answer 24

Yeah, use the "Attach File" button.

Answer 25

yes.. ll just state it..

if u is the initial velocity of m1
and m2 is stationary

and v1 is the final velocity of m1
and v2 the final velocity of m2

then

\[v1 = \frac{m_1-m_2}{m_1+m_2}u\]

so if m1 > m2.. v1 is same direction as u (cause they end up with same signs.. )

if m1< m2, v1 is opposite direction as u (cause v1 is negative of u)

and if m1 = m2, then v1=0

now i gotta scoot .. bye!

Answer 26

im sorry, there was a mistake in the initial question

Answer 27

theres another fact that the final velocity of object 1 is half the final velocity of object 2

Answer 28

now, is it always true that the obj1 cannot move in the positive direction?

Answer 29

It's dependent on the initial masses. Regardless of the velocity of object 1, if it is greater than object two, it will continue moving to the right. If it is equal to object two, it will stop. If it is less than object two, it will rebound.

Answer 30

i think its better if i post a picture of the question

Answer 31

question 65

Answer 32

Yup, I am certain that by Algebra you are capable of solving it. You have two equations and two unknowns.

Answer 33

So, you have your conservation of momentum in 1D expression, and the same for Kinetic Energy:

http://i.imgur.com/QzaqPsP.png

http://i.imgur.com/jHM49Up.png

Answer 34

yes thats what i tried solving but i took initial assumption that final velocity of obj2 is in the positive direction and i got an inconsistent value

Answer 35

Could you show me exactly what you did?

Answer 36

how would you solve it

Answer 37

sure

Answer 38

Use the Equation Editor if possible.

Answer 39

just a moment

Answer 40

its kinda long. is it ok if i attach a photo?

Answer 41

I'm still (slowly) looking over this, might be a minute.

Answer 42

ok

Answer 43

Oh!

Answer 44

?

Answer 45

head on collisions is when the objects come in opposite direction right?

Answer 46

Yup. I'm sorry, I thought I found a solution, but I didn't. This is really upsetting me that I can't figure this out though, lol, so I'm going to take a nap for a little, wake up and come back to it. If I can't figure it out by some time, I'll also start tagging some other people who are just better with algebra than me. It has to be somewhere in the algebra.

Answer 47

ok. thx a lot.

Answer 48

You intrinsically assumed.. that they must move in the same direction..
and also u assumed, that m1 must have twice speed as m2

in reality.. there are four cases that u can look at..
and try solving them..
whichever gives u nonsense answers like what u got.. is not possible :P.. (or requires infinitely big or zero mass).

i got two solutions which are possible!.. can u find it now?

Answer 49

@Mendicant_Bias its not ..algebra :D..

Answer 50

Really? This seems exactly like Algebra to me, which if we're not, demonstrating how would be good;

@physo , did you figure it out?

Answer 51

no i meant.. the algebra is not that difficult!

Answer 52

just take all cases possible and do it..

Answer 53

so i got the correct answer when i solved it with the assumption that object 1 moves in the opposite direction with twice the velocity of object 2. but in an exam, wouldn't it take too long to solve each cases? can we find a relationship between velocity and direction for elastic collision?

Answer 54

^Most questions I've found that are similar specify the direction of a velocity component. This question is a little unusual in not doing that, so I wouldn't be to worried about it as an exam question.

The fact that you have to "assume" their directions is really problematic IMO as a question in the first place.

Answer 55

@physo

Actually that question is just to make you understand the concept. All cases are possible. Both can go in the same direction too. But that requires that m1 is infinitely big compared to m2.. thats why you get the ratio to be either infinity or zero. So it has physical meaning.
So all four cases are very physical and possible. So there are four answers to this.
I guess the question was only to help you understand that.