# Ballistic Pendulum

1. Apr 6, 2005

### Fanman22

A 16 g rifle bullet traveling 170 m/s buries itself in a 3.2 kg pendulum hanging on a 2.5 m long string, which makes the pendulum swing upward in an arc. Determine the horizontal component of the pendulum's displacement.

I'm having trouble starting this problem. I know it's inelastic because kinetic energy is transformed into potential energy. I think I need to use this equation:

KE1 + PE1 = KE2 + PE2

Using that I can get the height that the block reaches. I need to find the horizontal displacement and I'm having trouble working the geometry because I don't know the angle above the x-axis. If I knew the angle, I could just use the equation:

Horizontal Displacement = h/tan(theta)

Any suggestions?

2. Apr 6, 2005

### Staff: Mentor

No. You know the collision is perfectly inelastic because the bullet gets buried in the block! But momentum is still conserved.

After the collision the "block + bullet" has some KE. That energy gets transformed into potential as it rises. (After the collision, energy is conserved.)

Work the problem in two stages.

3. Apr 6, 2005

### Fanman22

ok, I used mv/(m + M) = V....came to 0.8458m/s. So thats my initial velocity of the bullet/block system

The I used conservation of energy, KE=PE: .5(m + M)V^2 = (m + M)gh ....comes out to a height of 0.036m.

Now, I've got a triangle with the opposite side of theta being 0.036m. I need the adjacent.

But how do I find the theta?

4. Apr 6, 2005

### Staff: Mentor

Use some trig. Hint: the string length is given.

5. Apr 6, 2005

### Fanman22

I did this: SqRt. of ((2.5^2) + (2.464^2))...I get 3.51m. That answer niether makes sense, nor is it correct. Please take a look at my geometry in the pic I just made....

http://img.photobucket.com/albums/v225/Fanman22/triangle.jpg [Broken]

Last edited by a moderator: May 2, 2017
6. Apr 6, 2005

### Fanman22

*bump*

Just trying to get this solved before 6:15pm EST, I have to submit the answer and I can't stand getting something wrong (-7points) for what I know is a simple error.

7. Apr 6, 2005

### whozum

If theta is the angle where the block on the right is then:

Hypotenuse: 2.5
Opposite: 2.5-0.036 = 2.464

What trig functions can give you x? Theres 2.

Last edited: Apr 6, 2005
8. Apr 6, 2005

### Fanman22

I don't have theta, thats why I was using pythagorean theorum with the lengths that you can see in the pic I posted.

Also, the hypotenuse is 2.5, not 2.75, and the opposite is 2.464

9. Apr 6, 2005

### whozum

You can find theta with the information I just cited

10. Apr 6, 2005

### Fanman22

Oh jeez, sorry, I've been doing calculus and physics homework since 10am :yuck: ...I guess it's time for a break. Thanks though, I got it in just in time.