How Is the Maximum Swing Angle Determined in an Elastic Collision?

[babbagee]

Ok here is the problem

A ball with mass M moving horizontally at 5.00 m/s, collides elastically with a block with mass 3M that is initially hanging at rest from the ceiling on the end of a 50.0-cm wire.

Find the maximum angle through which the block swings after it is hit.

Ok what i tried was to see what the velocity of the two objects was when the first object hits the second one.

Mv_1i + 3Mv_2i = (4M)v_f

the velocity of the hanging object is going to be zero so that whole term cancels out.
i used this equation to find the final velocity, then i used the kenetic energy theorem

.5Mv² + 3Mgh = 4Mgh to solve for the height that the object swings up. But then i get stuck, because i think its asking me for the angle that the string makes when its at the maximum arc. Am I doing this the right way, if not can someone point me in the right direction.

Thanks

 

[mathmike]

if your collision is "inelastic" then

Mv1i + 3Mv2i = (4M)vf

but you say itis elastic so it has to be mv1i = mv1f + 3mv2f

 

[babbagee]

yeah i forgot its elastic, so the ball bounces back off. But how will i go about finding the angle.

 

[mathmike]

find the height the ball reaches then use some trig,

do you know how tho find the height?

 

[babbagee]

yeah, and i got an answer that did not seem right. I used the equation to find the final velocity of the block after it was hit by the ball. The velocity of the ball will -5m/s right after it hits the block because this is an elastic collision, or is that wrong. But any ways use the kenitic energy theorem. The block is going to have an intial kenetic energy but no potential energy and at the max height its going to have no kinetic energy but it is going to have potential energy. I solve for h right. And then i think use that value and subtract the value from the length of the string. And then use that as one of the sides and use the length of the string as the hypotensuse. But I am unsure of the part where i found the velocity to the block after it was hit by the ball becaue i assumed that he ball is going to have a velocity of -5.0m/s, would this be a correct assumption.

Thanks

 

[mathmike]

sounds like you got it congrat's

 

[Fermat]

It's an elastic collision, so the coefft of restitution, e, is 1.

Momentum Balance
==============
Mv1i + 0 = Mv1f + 3Mv2f
v1i = v1f + 3v2f ----------------------------- (1)

Elastic collision
============
e = 1
e = rel velocity after / rel velocity before = v2f - v1f / v1i
v1i = v2f - v1f --------------------------------(2)

Adding (1) and (2),

2v1i = 4v2f
v2f = 0.5*v1i = 0.5 * 5
v2f = 2.5 m/s
==========

also,

v1f = -2.5 m/s (it's going backwards)
===========