# Coservation of energy and impulse

1. May 4, 2010

### gongshow29

1. The problem statement, all variables and given/known data
A stream of elastic glass beads, each with a mass of 0.46 g, comes out of a horizontal tube at a rate of 108 per second. The beads fall a distance of 0.54 m to a balance pan and bounce back to their original height. How much mass must be placed in the other pan of the balance to keep the pointer at zero?

2. Relevant equations
1/2mv^2

3. The attempt at a solution
What I attempted was solving for the velocity of the ball as it hits the pan, then I multiplied by the mass, but Im not sure of how to account the rate.

2. May 5, 2010

### aim1732

Rate is necessary as force is momentum change per unit time. You need not think in terms of energy rather think of force acting on the pan as momenta lost by the beads PER UNIT TIME.

3. May 5, 2010

### sArGe99

The force on the pan will be 2*n*d/dt(m*v)
n being the number of beads hitting the pan per unit time.
v being the VERTICAL velocity of a bead as it hits the pan.

4. May 5, 2010

### aim1732

n is the rate here so don't you think d/dt(mv) is misleading?

5. May 5, 2010

### sArGe99

Yes it is. It should be 2*n*m*v?

6. May 5, 2010

Yes.

7. May 5, 2010

### gongshow29

Would I just use the conservation of energy to solve for the velocity then? Or momentum?

8. May 5, 2010

### Alter Baron

Use conservation of energy to find the velocity. Then use the velocity in the momentum calculation.

9. May 5, 2010

### gongshow29

so I would use the following setup mgh=1/2mv^2 correct?
I calculated my velocity with that setup
(0.46)(9.81)(0.54)=(1/2)(0.46)v^2
ended up with 3.254....
plugged that into the formula suggested which was 2(n)(m)(v):
2(108)(0.46)(3.254)=323g, but that is giving me the incorrect answer?
Where am I going wrong in my calculations?

Last edited: May 5, 2010
10. May 5, 2010

### Alter Baron

0.46g is in g; should be in kg.

11. May 5, 2010

### gongshow29

Ok, I switched out 0.46g into 0.00046kg, did the same calculation ended up with .010227kg, and my answer wants it in grams, so I multiplied it by 1000, for 10.227g, and its still incorrect. Im really confused now.

12. May 5, 2010

### Alter Baron

Re: conservation of energy and impulse

Ok, first of all, you should get a value of 0.323, but that is in Newtons.
Find the mass that is needed to balance that force.

13. May 5, 2010

### gongshow29

Ok that makes sense, appreciate everyone's help.