Ballistic Pedulum - Finding Kinetic Energy Lost

[ScoutFCM]

Here's a problem that I've been having trouble on for awhile and seem to be stuck. I was just wondering if someone could guide me or show me how to do this problem.

The Ballistic pendulum is a device usd to measure the speed of a fast-moving projectile such as a bullet. The bullet is fired into a large block of wood suspended from some light wires. The bullet is stopped by the block, and the entire system swings through the vertical distance, h. The mass of the bullet (m1=0.068kg), the mass of the pendulum (m2=0.256kg), h=6.2cm.

Vo=(.324kg/.068kg) x (2 x 9.8 m/s^2 x .062m)^1/2 = 5.25m/s

KEinitial= 1/2(.068kg x 5.25m/s)^2 = 0.937J

KEfinal= 1/2(.324kg) x (2 x 9.8 m/s^2 x .062m) = .197J

I got that far. I was wondering how do I find the kinetic energy lost from the info?

 

[jamesrc]

If I'm understanding your problem correctly, you're trying to solve for vo, the initial velocity of the bullet and the bullet/pendulum comes to a rest when it swings up to a height h.

Let's call the mass of the bullet m and the mass of the block M and let's set our datum for potential energy at the initial height of the bullet/pendulum.

First we need to consider the collision of the block and bullet using the conservation of momentum. This will give us the initial velocity of the ballistic pendulum:

m*vo = (m+M)v

Since we're neglecting things like air resistance and friction at the pendulum pivot, we know that all of this kinetic energy will be converted into potential energy:

.5*(M+m)v^2 = (M+m)*g*h

So find the expression for v in terms of vo, then plug into the 2nd equation to solve for vo.

If you need the kinetic energy lost in the collision, you can calculate the kinetic energy before and after:

KEb = .5*m*vo^2

KEa = .5*(M+m)*v^2

and find the difference.

 

[M98Ranger]

To find the kinetic energy lost in this problem, we can use the conservation of energy principle. This states that the total energy in a closed system remains constant, meaning that the initial kinetic energy of the bullet (KEinitial) is equal to the final kinetic energy of the combined system (KEfinal). Therefore, the kinetic energy lost can be calculated by subtracting the final kinetic energy from the initial kinetic energy.

In this case, the kinetic energy lost would be:

KElost = KEinitial - KEfinal

Substituting the values we have calculated, we get:

KElost = 0.937J - 0.197J = 0.74J

Therefore, the kinetic energy lost in this scenario is 0.74J. This means that the bullet lost 0.74J of its initial kinetic energy when it collided with the pendulum. This information can be useful in determining the speed of the bullet before it hit the pendulum, as well as other factors such as the efficiency of the collision and the amount of work done by the pendulum. I hope this helps guide you in solving the problem.