# Calculating Horizontal Displacement of Ballistic Pendulum

• Fanman22
In summary, 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. The horizontal component of the pendulum's displacement is 0.036 m.
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?

Fanman22 said:
I'm having trouble starting this problem. I know it's inelastic because kinetic energy is transformed into potential energy.
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.

ok, I used mv/(m + M) = V...came to 0.8458m/s. So that's 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?

Fanman22 said:
But how do I find the theta?
Use some trig. Hint: the string length is given.

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

Last edited by a moderator:
*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.

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:
I don't have theta, that's 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

You can find theta with the information I just cited

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

## 1. How is the horizontal displacement of a ballistic pendulum calculated?

The horizontal displacement of a ballistic pendulum can be calculated by using the equation d = (l + x) tanθ, where d is the horizontal displacement, l is the length of the pendulum, x is the vertical displacement, and θ is the angle of the pendulum at the point of impact.

## 2. What is the purpose of calculating the horizontal displacement of a ballistic pendulum?

The purpose of calculating the horizontal displacement of a ballistic pendulum is to determine the initial velocity of a projectile. This is useful in various fields such as ballistics, physics, and engineering.

## 3. Can the horizontal displacement be negative?

Yes, the horizontal displacement can be negative. This indicates that the projectile landed behind the point of impact on the pendulum, which can happen due to factors such as air resistance and imperfections in the pendulum's swing.

## 4. Does the height of the pendulum affect the calculation of horizontal displacement?

No, the height of the pendulum does not affect the calculation of horizontal displacement. This is because the equation used to calculate the displacement takes into account the length of the pendulum, not its height.

## 5. What are some potential sources of error when calculating the horizontal displacement of a ballistic pendulum?

Some potential sources of error when calculating the horizontal displacement of a ballistic pendulum include air resistance, imperfections in the pendulum's swing, and human error in measuring the angle and length of the pendulum. It is important to minimize these errors for accurate results.

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