# Derivation of Momentum

1. Aug 14, 2015

### Depasquale97

1. The problem statement, all variables and given/known data
A heavy mallet of Mass M (see Attached file) is dropped and moves through vertical distance y before it hits the top of a tent stake of mass m, driving it into the ground a distance d. Assume that the ground offers a a constant resistance to the motion of the tent stake and mallet, which move together after impact.
Show that the combined velocity, vc, of the mallet and the tent stake after impact in terms of the mass of the mallet M, the mass of the stake m and the velocity of the mallet before impact v is given by
vc=v/(1+m/M)

2. Relevant equations

3. The attempt at a solution
I tried to use the equation; Total momentum before collision = Total momentum after collision but had no success.

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2. Aug 14, 2015

### RUber

You know that at the point of impact the momentum of the mallet is Mv and that momentum is transferred to the combined system as (M+m)v_c. Is any momentum lost?
If not, do the algebra.

3. Aug 14, 2015

### Depasquale97

Thank you RUber, no momentum is lost.

4. Aug 14, 2015

### RUber

So then you need to show that
$Mv = (M+m)v_c \iff v_c = \frac{v}{1+\frac{m}{M}}$
Do this by isolating v_c and rewriting (M+m) as M(1+m/M).

5. Aug 14, 2015

### Depasquale97

Thank you very much, much appreciated