Ballistic Pendulum results.

1. Nov 6, 2011

QuarkCharmer

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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.

2. Nov 6, 2011

I like Serena

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

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).

Yep.

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

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

Yep.

3. Nov 6, 2011

QuarkCharmer

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?

4. Nov 6, 2011

I like Serena

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

5. Nov 6, 2011

QuarkCharmer

I'm talking about after the collision has occured 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?

6. Nov 6, 2011

I like Serena

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.

7. Nov 6, 2011

I like Serena

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.

8. Nov 6, 2011

QuarkCharmer

Thank you, that answers my question perfectly!

9. Nov 6, 2011

I like Serena

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.

10. Feb 27, 2012

Newsakai

Re: the initial velocity of ball

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).