Ballistics pendulum on steroids

[Vb1702]

Homework Statement

I am doing a science fair experiment using a ballistics pendulum. Instead of a wooden block to fire into I am using ballistics gelatin. This will allow me to measure the amount of energy deposited into the gelatin. A ballistics pendulum is usually used to determine velocity but I want to determine the amount of energy. I can determine velocity using available data. Most of the data on ballistics pendulums indicates the collision is inelastic. I assume this is because all of the energy is deposited into the wooden block. I believe in this instance the collision will be elastic, not perfectly elastic, since the two objects will move independently after the collision. The gelatin will initially move with the bullet but then the bullet will continue on and the gelatin will return to its original position.

Homework Equations

KEi= 1/2m vo^2

where m = mass of bullet and vo = the initial velocity of the bullet

KEf = 1/2 (m+M) vf^2

where M = mass of pendulum and vf = velocity of pendulum and ball

PEf = (m+M)(g)(h)

where g = gravitational acceleration
and h = change in height of gel block

The Attempt at a Solution

It seems like I should be able to just use the equation PEf = (m+M)(g)(h) to determine the kinetic energy converted to potential energy in the gel block but the more I read the less sure I am about this. I don't have any data yet as I am just in the research stage. I just need to determine if I'm right about this being an elastic collision and using the PEf equation to determine the amount of energy deposited into the gel.

Maybe, since kinetic energy is being converted to internal energy (in the gel block) and potential energy I can't determine the amount of energy deposited? Maybe, this is conservation of momentum and not conservation of energy? Maybe I'm in over my head!

Help!

Thanks for your help.

 

[pgardn]

Seems a bit experimentally complicated as ballistic pendulums usually are used for perfectly inelastic collisions.

I have a suggestion:

How about firing your projectile off a perfectly horizontal table against a wall marked with a line (height of the table). If you know the height of the table and you know how far down the wall the projectile dropped if it makes an imprint on the wall you can determine the velocity of the projectile. You can measure delta x (distance from the table to the wall) and you know delta y (the distance the projectile dropped while in the air, the diffrence between the height of the table and how far down the wall the projectile hit). The delta x gives you horizontal distance and the delta y can yield the time the projectile is in the air. This allows you to calculate V initial and its all Vx cause you shot the projectile horizontally.

Repeat the same experiment through the gel. The projectile should hit further down on the wall which means its spent more time in the air which means it was going slower giving you a diff V initial.

Then using the two diff. V's calculate the kinetic energy and the diff between the two which would mostly be the loss of mechanical energy while traveling through the gel.

I think this would be lots easier.

 

[kerimek]

It sounds like you have a very interesting experiment planned. It is always great to see students pushing the boundaries and exploring new ideas.

First, let's address the concept of using a ballistics pendulum on steroids. This means that you are taking a traditional experiment and modifying it to enhance its capabilities. In this case, you are using ballistics gelatin as the target instead of a wooden block. This modification will allow you to measure the energy deposited into the gelatin, which is a more accurate representation of the impact of a bullet compared to a wooden block. This is a clever and innovative idea, and it shows that you are thinking critically about your experiment.

Now, let's discuss the concept of using a ballistics pendulum to determine the amount of energy deposited instead of just the velocity. As you mentioned, most data on ballistics pendulums indicates an inelastic collision, where all of the energy is deposited into the wooden block. However, in this case, the collision will be elastic, meaning that the two objects (bullet and gelatin) will move independently after the collision. This makes it more challenging to determine the amount of energy deposited into the gelatin.

In terms of equations, you are correct in using the equation PEf = (m+M)(g)(h) to determine the potential energy in the gel block. However, as you mentioned, this does not take into account the internal energy that is produced in the gelatin. This is because some of the kinetic energy of the bullet will be converted into heat and sound as it penetrates the gelatin. Therefore, you cannot directly determine the amount of energy deposited into the gelatin using this equation.

Instead, you may want to consider using the concept of conservation of momentum. This means that the total momentum before the collision (bullet and pendulum) will be equal to the total momentum after the collision (bullet and pendulum moving independently). This can be expressed as mvo = (m+M)vf, where vo is the initial velocity of the bullet and vf is the velocity of the bullet and pendulum after the collision. By measuring vf, you can then calculate the amount of energy deposited into the gelatin using the equation KEf = 1/2 (m+M) vf^2.

In conclusion, your idea of using a ballistics pendulum on steroids is a great one, and it will allow you to measure the energy deposited into the gelatin. However, you may