# Dynamics - Collision Question

1. Homework Statement

http://img138.imageshack.us/img138/9476/phyus3mu7.jpg [Broken]​
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2. Homework Equations

Conservation of momentum
Conservation of kinetic energy

3. The Attempt at a Solution

I really have no idea. I dont know the velocity of A before the collision and i dont know the speed of A after the collision. So i cant use the conservation of momentum. I also know its not an elastic collision because im told "the restitution is e=0.5". Should i have been told some kind of equation to allow me to work this out or am i missing something?

James

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Shooting Star
Homework Helper
2. Homework Equations

Conservation of momentum
Conservation of kinetic energy
Both. In short, (don't feel like using latex), if co-eff of restitution is e=1/2, then,

relative velo after collision = vb - va_f = (1/2)va_i = relative velo before collision.

Using consvn of mom, ma*va_i = ma*va_2 + mb*vb.

All velos are +ve to the RHS. Solve for va_f. The masses and vb are given.

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Hi shooting star, i really appreciate the help but im still a little stuck, would you mind answering a few more questions for me?

ma*va_i = ma*va_2 + mb*vb
Is this correct:
ma = Mass A = 1kg
va_i = Velocity of A initially = Unknown
va_2 = Final velocity of A? = Unknown
mb = Mass of B = 10kg
vb = Final Velocity of B? = 0.876m/s

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relative velo after collision = vb - va_f = -(1/2)va_i = -relative velo before collision
Im also a little confused by this equation. Does that mean that in effect relative velo after collision is equal to -relative velo before collision?

Or was it meant to read like this:
relative velo after collision = vb - va_f
-(1/2)va_i = -relative velo before collision
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Finally, am i meant to rearrange this equation
vb - va_f = -(1/2)va_i
to make vb the subject and then factor it into the conservation of momentum equation you gave me? I only ask because i still have two unknowns at this point, va_i and va_f.

Again thank you for the help, sorry i have to ask more questions.

The coefficient of restitution between to objects (1 and 2) is given by
$$C_r = \frac{V_{2f}-V_{1f}}{V_{1i}-V_{2i}}$$

If A is object 1 and B is object 2, then this simplifies to:
$$.5 = \frac{V_{Bf}-V_{Af}}{V_{Ai}}$$
Since the initial velocity of B is zero.

And then you have
$$M_{A}V_{Ai} = M_{A}V_{Af}+M_{B}V_{Bf}$$
I think Shooting Star may have meant solve for $$V_{Af}$$. Looks like you can do it with those two equations.

Shooting Star
Homework Helper
Is this correct:
ma = Mass A = 1kg
va_i = Velocity of A initially = Unknown
va_2 = Final velocity of A? = Unknown
mb = Mass of B = 10kg
vb = Final Velocity of B? = 0.876m/s
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All correct. Sorry I made a few typos in my last post. I have edited those. Pl go through it now once more. Two simple eqns and two unknowns -- piece of cake.

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Thank you both for the help. For some reason or another i wasnt given these equations. Ill give it a go tomorrow and see how it goes.

That worked :D