# Finding velocity and momentum of a bullet and recoiling gun

• C-ron27
In summary, a bullet with a kinetic energy of 90 J leaves the barrel of a gun with a mass of 4 kg and travels 50 cm. The bullet has a mass of 10 g. Using the equations KE = 1/2mv^2 and p = mv, the final velocity of the bullet is found to be 134.16 m/s and its final momentum is 1.3416 kg m/s. The momentum of the recoiling gun is found to be -0.3354 m/s, using conservation of momentum. The kinetic energy of the recoiling gun is calculated to be 0.225 J. The given barrel length of 50 cm is not necessary for these calculations.
C-ron27

## Homework Statement

A bullet leaves the barrel of a gun with a kinetic energy of 90 J. The barrel of the gun is 50 cm long. The gun has a mass of 4 kg, the bullet 10 g. (a) Find the bullets final velocity. (b) Find the bullets final momentum. (c) Find the momentum of the recoiling gun. (d) Find the kinetic energy of the recoiling gun.

KE = 1/2mv^2
p = mv

## The Attempt at a Solution

(a) Since I know the kinetic energy of the bullet as it leaves the barrel, I attempted to find the velocity with this information.

90 J = (1/2)(.01 kg)v^2
which gives v = 134.16 m/s

(b) To find momentum of the bullet I plugged this value for v into p= mv, this gives the result p = 1.3416 kg m/s.

for (c) I used conservation of momentum, since the initial momentum of both the bullet and gun are zero.
0 = (1.3416 kg m/s) + (4 kg)v
solving this give v = -.3354 m/s

(d) KE =(1/2)mv^2 so the kinetic energy of the gun is KE = (1/2)(4 kg)(-.3354 m/s)^2 = .225 J

I'm not entirely sure if I solved this correctly. My main problem is that it gives the length of the barrel of the gun and I did not use this in the solution. Is this unnecessary information? or did I do this incorrectly? I thought that the 50 cm could be used to find the work done on the gun, but 50 cm is how far the bullet moved, not how far the gun moved.

Welcome to Physics Forums!

Your calculations look good. The barrel length is irrelevant as you have surmised. You might want to round your results to better reflect the number of significant figures provided in the given data.

In future, please retain the formatting template headings when you put together your post. I've re-inserted the headers for you this time.

Thank you very much! I planned to round my final results but just kept them that way in case I needed to use them in further calculations. Thanks again for the input!

## 1. How do you measure the velocity of a bullet?

To measure the velocity of a bullet, you can use a device called a chronograph. This device uses sensors to detect the bullet passing through and calculates its velocity based on the time it takes to travel between the sensors. Another method is to use a high-speed camera to capture the bullet's movement and then analyze the footage to determine its velocity.

## 2. What factors affect the velocity of a bullet?

The velocity of a bullet can be affected by several factors, including the type of gun and ammunition used, the weight and shape of the bullet, the temperature and humidity of the environment, and the barrel length and condition of the gun.

## 3. How is momentum calculated for a bullet and a recoiling gun?

Momentum is calculated by multiplying the mass of an object by its velocity. To calculate the momentum of a bullet, you would need to know its mass and velocity. For a recoiling gun, you would need to know the mass of the gun and the velocity at which it recoils.

## 4. Why is it important to know the velocity and momentum of a bullet and recoiling gun?

Knowing the velocity and momentum of a bullet and recoiling gun is important for various reasons. It can help in determining the effectiveness of a gun and its ammunition, analyzing the impact of a bullet on a target, and understanding the recoil force that a shooter experiences when firing a gun.

## 5. Can the velocity and momentum of a bullet and recoiling gun be affected by external forces?

Yes, the velocity and momentum of a bullet and recoiling gun can be affected by external forces such as wind, air resistance, and gravity. These forces can alter the trajectory and speed of the bullet and the recoil of the gun, making it important to consider them when calculating and analyzing the velocity and momentum of a bullet and recoiling gun.

• Introductory Physics Homework Help
Replies
21
Views
1K
• Introductory Physics Homework Help
Replies
10
Views
1K
• Introductory Physics Homework Help
Replies
10
Views
10K
• Introductory Physics Homework Help
Replies
31
Views
3K
• Introductory Physics Homework Help
Replies
2
Views
264
• Introductory Physics Homework Help
Replies
7
Views
1K
• Introductory Physics Homework Help
Replies
13
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
871
• Introductory Physics Homework Help
Replies
10
Views
3K
• Introductory Physics Homework Help
Replies
6
Views
512