# Is the Ballistic Pendulum a Conservative Process?

• QuarkCharmer
In summary: The process of the ballistic pendulum is a nonconservative one, in that energy is lost in the form of heat, sound, and other forms. However, momentum is conserved throughout the process.
QuarkCharmer

## Homework Statement

I was just wondering if someone would be kind enough to look over these solutions and tell me if I am correct. The lab was a simple ballistic pendulum, which I am sure every physics student performs.

## The Attempt at a Solution

1.) Compare/contrast elastic and inelastic collisions.

During an elastic collision, both energy and momentum are conserved. During an inelastic collision, momentum is conserved, but energy is not.

2.) Where did the energy lost during the collision between the projectile and the receiver go?

The energy lost during the collision between the projectile and the reciever was dissipated in the form of heat, sound, vibration, et al.

3.) During what portions of this process is momentum conserved?

Momentum is conserved prior to, and immediately after the inelastic collision between the projectile and the pendulum.

4.) During what portions of this process is energy conserved?

Energy is always conserved. However, if you were to treat this process as it’s own system, and consider energy lost due to heat, sound, and other things “lost”, then energy would be conserved from the start of the process, to the time just before the ball strikes the pendulum. It would also be conserved after the projectile and mass attain their initial kinetic energy from the collision and continue on to the point in which that kinetic energy is transferred into potential energy at it’s maximum height.

5.) Overall, is the operation of the ballistic pendulum a conservative or non conservative process?

Overall, I would say that the operation of the ballistic pendulum is a non conservative process, because some energy is lost from the process/system in the form of heat, sound, and other forms during the collision.

QuarkCharmer said:

## Homework Statement

I was just wondering if someone would be kind enough to look over these solutions and tell me if I am correct. The lab was a simple ballistic pendulum, which I am sure every physics student performs.

I must have been an unusual physics student, because this is the first time I've heard of a ballistic pendulum.

QuarkCharmer said:
1.) Compare/contrast elastic and inelastic collisions.

During an elastic collision, both energy and momentum are conserved. During an inelastic collision, momentum is conserved, but energy is not.

Momentum and energy are both *always* conserved.
"Kinetic" energy is not necessarily conserved, since it can typically be converted to other types of energy (like heat).

QuarkCharmer said:
2.) Where did the energy lost during the collision between the projectile and the receiver go?

The energy lost during the collision between the projectile and the reciever was dissipated in the form of heat, sound, vibration, et al.

Yep.

QuarkCharmer said:
3.) During what portions of this process is momentum conserved?

Momentum is conserved prior to, and immediately after the inelastic collision between the projectile and the pendulum.

Trick question?
When you shoot the bullet, you are thrown backward, and you in turn transfer your backward momentum to the earth.

QuarkCharmer said:
4.) During what portions of this process is energy conserved?

Energy is always conserved. However, if you were to treat this process as it’s own system, and consider energy lost due to heat, sound, and other things “lost”, then energy would be conserved from the start of the process, to the time just before the ball strikes the pendulum. It would also be conserved after the projectile and mass attain their initial kinetic energy from the collision and continue on to the point in which that kinetic energy is transferred into potential energy at it’s maximum height.

I'd stick to "Energy is always conserved."
You can mention "kinetic" energy is converted to potential energy, heat, e.a.

QuarkCharmer said:
5.) Overall, is the operation of the ballistic pendulum a conservative or non conservative process?

Overall, I would say that the operation of the ballistic pendulum is a non conservative process, because some energy is lost from the process/system in the form of heat, sound, and other forms during the collision.

Yep.

I think they are talking specifically as if the pendulum and projectile were the only occupants in one system.

I'm still not quite sure how momentum is conserved when the pendulum begins to swing.

It can be modeled by:

Kinetic energy before = Potential energy after:
$$\frac{1}{2}mv^{2} = mgh$$

If momentum is simply the product of mass and velocity, then at the same time as the above equation:
$$mv_{before} = mv_{after}$$

But the "after" velocity would be zero, and thus momentum is lost somewhere?

Your mixing up masses.

Let's say the projectile has mass m and the bob of the pendulum has mass M.

Then:
$$m v_{before} = (M+m) v_{after}$$

and:
$${1 \over 2} m (v_{before})^2 = {1 \over 2} (M+m) (v_{after})^2 + \text{ energy converted to heat e.a.}$$

Furthermore:
$${1 \over 2} (M+m) (v_{after})^2 = (M+m) g h$$

I'm talking about after the collision has occurred and the pendulum is simply swinging upwards. Both before and after the swing, the mass m is the combined mass of the projectile and the pendulum.

I suppose, basically I am asking "Does the conservation of momentum only apply during a collision?

QuarkCharmer said:
I'm talking about after the collision has occurred and the pendulum is simply swinging upwards. Both before and after the swing, the mass m is the combined mass of the projectile and the pendulum.

I suppose, basically I am asking "Does the conservation of momentum only apply during a collision?

Oh, okay.
In that case the momentum is transferred to the pendulum as a whole, and on to the earth.
You may have noticed that the pendulum shakes a little bit while swinging.

QuarkCharmer said:
I suppose, basically I am asking "Does the conservation of momentum only apply during a collision?

Here we're getting into the trick questions and nitpicking.

Conservation of momentum always applies.

But to model the ballistic pendulum, we will treat it such that at collision conservation of momentum applies and kinetic energy is lost.
And after the collision, we will treat it such that kinetic and potential energy together are conserved, and momentum is not.

Thank you, that answers my question perfectly!

Note that in physics we usually start with a "simple" model.
And then, when we want to do high precision measurements, we will need to make corrections, and corrections on corrections to compensate for the things we neglect at first.

A typical correction to make in a pendulum is in the length of the string and measuring equipment that change with temperature.

when the mass of ball increases, the the angle of the pendulum increases and the initial velocity increases.
Why??
Isnt it when mass of ball increases, the initial velocity decreases?? Since the initial force applied is the same(the force of the spring).

## 1. How does a ballistic pendulum work?

A ballistic pendulum is a device used to measure the velocity of a projectile by measuring the height to which it rises after impacting a pendulum. The kinetic energy of the projectile is transferred to the pendulum, causing it to rise to a certain height. By measuring this height and using conservation of energy equations, the initial velocity of the projectile can be calculated.

## 2. What is the purpose of using a ballistic pendulum?

The purpose of using a ballistic pendulum is to accurately measure the velocity of a projectile. This can be useful in various scientific experiments, such as studying the effects of air resistance on the velocity of a projectile or determining the velocity of a bullet fired from a gun.

## 3. How is the height of the pendulum related to the initial velocity of the projectile?

According to conservation of energy, the initial kinetic energy of the projectile is equal to the potential energy of the pendulum at its maximum height. Therefore, by measuring the height of the pendulum, the initial velocity of the projectile can be calculated using the equation KE = PE.

## 4. What factors can affect the accuracy of ballistic pendulum results?

There are several factors that can affect the accuracy of ballistic pendulum results, including air resistance, friction in the pivot point of the pendulum, and the accuracy of the measurements taken. It is important to minimize these factors and take multiple measurements to obtain more accurate results.

## 5. Can a ballistic pendulum be used to measure the velocity of any projectile?

While a ballistic pendulum can be used to measure the velocity of most projectiles, there are some limitations. The projectile must be relatively small and the impact must be inelastic, meaning the projectile will not bounce off the pendulum. Additionally, the pendulum must have enough mass to be able to detect the impact and rise to a measurable height.

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