# Ballistic pendulum, finding final height

1. Mar 5, 2012

### jorcrobe

1. The problem statement, all variables and given/known data

3. The attempt at a solution

I used conservation of momentum for the initial velocity of mass 2, and conservation of mechanical energy for the movement from rest to highest position, KE=PE.

The answer that I received is selected in the screenshot. However, when the calculations were completed, I received a value of 1.81m... Which is longer than the string. Does anyone spot my problem? Thank you.

2. Mar 5, 2012

### Ericv_91

Explain why KE=PE at the highest position.

3. Mar 5, 2012

### jorcrobe

So, the KE is not being conserved as PE? I see that there is also a horizontal displacement.

4. Mar 5, 2012

### Ericv_91

Forget what I said, I misread/misunderstood your explanation. Yes, energy is conserved here.

When you are calculating h from the potential energy equation, what does h represent?

5. Mar 5, 2012

### jorcrobe

The distance from the x axis, y=0.

6. Mar 5, 2012

### Ericv_91

Right. y=0, which is the position where the ball is hanging, to the position where the ball is at a max height. One would assume that to create an equation relating this height to the distance between the ball and the ceiling, you would need to have the variable L somewhere in the equation you choose. Right?

7. Mar 5, 2012

### jorcrobe

Well, I used the first equation, and I am receiving a negative number.

Why is it that when I solved for h, it was a number greater than the maximum height, L?

I'm very sorry, I had never taken physics before this course.

8. Mar 5, 2012

### Staff: Mentor

When you say "The answer I received", do you mean that you were given this as a correct answer, or that it is the answer you obtained by working the problem? The reason that I ask is that to me the selected option doesn't appear to be a correct answer for the given problem.

If the change of elevation of the second ball, as computed from the "randomized variables" happens to be greater than the length of string, what can you conclude will happen? What will be the minimum separation of ceiling and ball?

9. Mar 5, 2012

### Ericv_91

Unless I've made a terrible mistake in my calculations, it seems as though either the question gave you a wrong number for the length of the string, or somehow the ball will go above the height of the pendulum, even though there is a ceiling in the way.