# Momentum conservation (ballistic pendulum)

• jakec
In summary, the conversation discusses a scenario where a .01kg bullet is fired into a 1.2kg block hanging from a 1m wire. The bullet exits the block with a speed of 200m/s and the block swings to a height of .2 meters. The original velocity of the bullet is found to be 201.2 m/s and the percentage of original energy remaining in mechanical forms is approximately 99%. The conversation also includes discussions on energy conservation and the calculation of the momentum of the block.
jakec

## Homework Statement

A .01kg bullet is fired into a 1.2kg block hanging from a 1m wire. The bullet exits the block with a speed of 200m/s and the block swings to a height of .2 meters. What is the original velocity of the bullet? What percentage of the original energy of the bullet is no longer in mechanical forms of energy?

## Homework Equations

I know that initial momentum = final momentum but I can't seem to find the velocity of the block after the collision.

## The Attempt at a Solution

I had this on a test and tried energy conservation. Obviously this isn't correct but I can't find the momentum of the block. I've been working this for about 5 hours now so I'm clearly not getting something so a step by step explanation would be great.
[/B]
GPE of block = (mgh) = (1.2 x 9.8 x 0.2m) = 2.353 Joules. This has resulted from KE of the bullet having swung the block.
The bullet exited the block. Its KE after exit = 1/2 (m*v^2) = 1/2 (0.01*200^2) = 200 Joules.
The total energy has come from the bullet, = (200 + 2.353) = 202.353 Joules.
Original bullet V = sqrt.(2KE/m) = sqrt.(404.706/0.01) = 201.2 m/sec.

jakec said:
GPE of block = (mgh) = (1.2 x 9.8 x 0.2m) = 2.353 Joules.
That's the energy of the block after the bullet has passed through it. Use this to determine the speed of the block.

Ok, so this is what I ended up with:

mgh = 1/2mv2
v=sqrt(2gh) = 1.98m/s

Pi = Pf
mpvpi = mbvb + mpvpf
vpi = (mbvb + mpvpf) / mp
vpi = 437.6 m/s

Thanks for the help!

## 1. What is momentum conservation?

Momentum conservation is a fundamental law of physics that states that the total momentum of a closed system remains constant. This means that in a closed system, the total amount of momentum before an event (such as a collision) is equal to the total amount of momentum after the event.

## 2. How does momentum conservation apply to a ballistic pendulum?

In a ballistic pendulum, the projectile (such as a bullet) collides with a stationary pendulum, causing it to swing upwards. According to the law of momentum conservation, the total momentum before the collision is equal to the total momentum after the collision. This means that the momentum of the projectile + the momentum of the pendulum before the collision is equal to the momentum of the pendulum after the collision.

## 3. Why is the ballistic pendulum used to measure the velocity of a projectile?

The ballistic pendulum is used to measure the velocity of a projectile because it allows us to use the law of momentum conservation to calculate the velocity of the projectile. By measuring the height and mass of the pendulum after the collision, we can calculate the momentum and then use it to solve for the initial velocity of the projectile.

## 4. What are the assumptions made in a ballistic pendulum experiment?

Some of the common assumptions made in a ballistic pendulum experiment include: neglecting air resistance, assuming the collision between the projectile and the pendulum is elastic, and assuming that the pendulum's mass is much greater than the projectile's mass. These assumptions allow for a simpler calculation and increase the accuracy of the results.

## 5. How can momentum conservation be applied to real-life situations?

Momentum conservation is a fundamental law of physics and can be applied to various real-life situations. For example, it can be used to analyze car crashes and determine the velocity of the cars involved. It can also be applied to sports, such as when a hockey player hits a puck with a stick, the total momentum of the system (player + puck) remains constant. Understanding momentum conservation can help us predict and understand the outcome of various physical events.

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