Impulse/momentum/collision question

[dnt]

Homework Statement

basically a cue ball is struck by a cue, and that ball travels (without friction) and hits another ball (which isn't moving initally). they give all the masses and the impulse of the cue hitting the first ball. they tell us its an elastic collision.

Homework Equations

p=mv
I=change in momentum

The Attempt at a Solution

ok its easy to get the initial speed of the first ball using the impulse/momentum equation. and i know since its frictionless the ball doesn't change speed.

so basically a ball hits a 2nd ball (both have the same mass)...how do you mathematically find the final speed? i know the 2nd ball will have the same velocity as the first one but how do you show it in equations?

momentum: (initials) m1v1 + m2v2 = (finals) m1v1 + m2v2

the first v2 is 0 (2nd ball isn't moving) and all the masses cancel but you only get:

v1i = v1f + v2f

if you use conservation of kinetic energy you get basically the same thing (only the v's are squared).

what do you do with that since the only thing we know (out of 3 variables) is the initial velocity of the first ball?

(also couldn't we assume it was elastic since the two balls didnt stick together?)

 

[dnt]

anyone?

 

[PhanthomJay]

Homework Statement

basically a cue ball is struck by a cue, and that ball travels (without friction) and hits another ball (which isn't moving initally). they give all the masses and the impulse of the cue hitting the first ball. they tell us its an elastic collision.

Homework Equations

p=mv
I=change in momentum

The Attempt at a Solution

ok its easy to get the initial speed of the first ball using the impulse/momentum equation. and i know since its frictionless the ball doesn't change speed.

so basically a ball hits a 2nd ball (both have the same mass)...how do you mathematically find the final speed? i know the 2nd ball will have the same velocity as the first one but how do you show it in equations?

momentum: (initials) m1v1 + m2v2 = (finals) m1v1 + m2v2

the first v2 is 0 (2nd ball isn't moving) and all the masses cancel but you only get:

v1i = v1f + v2f

if you use conservation of kinetic energy you get basically the same thing (only the v's are squared).

what do you do with that since the only thing we know (out of 3 variables) is the initial velocity of the first ball?

(also couldn't we assume it was elastic since the two balls didnt stick together?)

when the 2 balls don't stick, the collision could be elastic or inelastic, depending on whether any energy is lost during the collision. In a perfectly (ideal) elastic collision, such as is given in this problem, energy is conserved as well as momentum. Conservation of energy gives you a second equation, which will allow you (with some difficulty) to solve the 2 unknowns v1f and v2f.

 

[ashishsinghal]

conservation of energy may be quite bothering. You can use another method. Since collision is elastic, the bodies have the same speed of separating as that of approaching.see http://en.wikipedia.org/wiki/Coefficient_of_restitution
this means,
v2(f)-v1(f) = v1(i)
now you have two equations in two variables. solve them

 

[rwisz]

You are correct in using the conservation of momentum equation to solve this problem. Since the collision is elastic, the total momentum before the collision will equal the total momentum after the collision. This can be written as:

m1v1i + m2v2i = m1v1f + m2v2f

Since the second ball is initially at rest, its initial velocity (v2i) is 0. Also, since the two balls have the same mass, we can simplify the equation to:

v1i = v1f + v2f

So, we have two unknown variables (v1f and v2f) and only one equation. However, we also know that the two balls have the same final velocity (since they stick together after the collision). This can be written as:

v1f = v2f

Now, we have two equations and two unknowns, which we can solve simultaneously. Substituting v1f = v2f into the first equation, we get:

v1i = 2v1f

Solving for v1f, we get:

v1f = v1i/2

Therefore, the final velocity of both balls will be half of the initial velocity of the first ball. This can also be confirmed using the conservation of kinetic energy equation, which gives us the same result.

In conclusion, the final velocity of both balls will be half of the initial velocity of the first ball, since they have the same mass and the collision is elastic. This means that the second ball will also have the same final velocity as the first ball.