# How Fast Was the Bullet After Passing Through the Ballistic Pendulum?

• shigami117
Kinetic energy is 1/2mv^2, and potential energy is mgh.So, in summary, using conservation of energy and momentum, we can determine the velocity of a bullet as it emerges from a block in a ballistic pendulum. This is done by equating the initial kinetic energy of the bullet with the final kinetic energy and potential energy of the block.
shigami117
1. A 9.05- g bullet from a 9-mm pistol has a velocity of 331.0 m/s. It strikes the 0.705- kg block of a ballistic pendulum and passes completely through the block. If the block rises through a distance h = 19.47 cm, what was the velocity of the bullet as it emerged from the block? i know that this is supposed to be done using conservation of energy and momentum. but i can't get it

It's still a conservation of energy.

Initial kinetic energy of bullet + initial potential energy of block (which is zero) -> final ke of bullet + final potential energy of block.

Hi there,

I understand you are struggling with solving this problem using conservation of energy and momentum. Let me walk you through the steps to help you understand the solution.

First, let's define our variables. We have a bullet with a mass of 9.05 g (0.00905 kg) and a velocity of 331.0 m/s. It strikes a block with a mass of 0.705 kg and causes it to rise through a distance of 19.47 cm (0.1947 m). We want to find the velocity of the bullet as it emerges from the block, let's call it v'.

Now, let's apply conservation of momentum. We know that momentum is conserved in a closed system, so the total momentum before the collision must equal the total momentum after the collision. In this case, the bullet is the only object moving before and after the collision, so we can write:

m1v1 = m1v1' + m2v2'

Where m1 is the mass of the bullet, v1 is its initial velocity, m2 is the mass of the block, v1' is the velocity of the bullet after the collision, and v2' is the velocity of the block after the collision.

Substituting our values, we get:

(0.00905 kg)(331.0 m/s) = (0.00905 kg)(v') + (0.705 kg)(v2')

Now, let's apply conservation of energy. We know that the total energy before the collision (kinetic energy of the bullet) must equal the total energy after the collision (kinetic energy of the bullet and block). So we can write:

(1/2)m1v1^2 = (1/2)m1v1'^2 + (1/2)m2v2'^2

Substituting our values, we get:

(1/2)(0.00905 kg)(331.0 m/s)^2 = (1/2)(0.00905 kg)(v')^2 + (1/2)(0.705 kg)(v2')^2

Now, we have two equations with two unknowns (v' and v2'). We can solve for one of the variables and then substitute it into the other equation to solve for the other variable.

Let's solve for v2' first. Rearranging the momentum equation, we get:

## 1. What is a ballistic pendulum?

A ballistic pendulum is a device used to measure the velocity of a projectile. It consists of a pendulum with a known mass and a target, typically made of a soft material such as clay or putty, that the projectile will hit and stick to.

## 2. How does a bullet through ballistic pendulum experiment work?

In this experiment, a bullet is fired into the target of the ballistic pendulum. The bullet will stick to the target, causing the pendulum to swing upwards. The height of the pendulum's swing can then be measured and used to calculate the velocity of the bullet before impact.

## 3. What factors can affect the accuracy of the results in a bullet through ballistic pendulum experiment?

The accuracy of the results in this experiment can be affected by factors such as air resistance, friction, and the elasticity of the target material. The accuracy can also be impacted by any errors in measurement or calculation.

## 4. What are the applications of a ballistic pendulum?

A ballistic pendulum can be used in forensic science to determine the velocity and trajectory of a bullet in a crime scene. It can also be used in physics education to demonstrate principles of momentum and energy conservation.

## 5. How can the results of a bullet through ballistic pendulum experiment be improved?

To improve the accuracy of the results, multiple trials should be conducted and the average value should be calculated. Additionally, using a more sensitive measuring device and minimizing external factors such as air resistance can also improve the results.

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