Ballistic Pendulum and Rotational Dynamics

I. Blackwood (Ballistic) Pendulum

1. With the pendulum catch system out of the way fire the ball into the box at least ten times. In each case find vo, the initial velocity of the ball; po, the initial linear momentum; and Lo, the initial angular momentum relative to the axis of rotation. Notice that:

where R is the horizontal range and h the vertical distance traveled by the ball from the gun to the impact point in the box.

2. Determine the moment of inertia of the "physical pendulum" formed by the ball+bob system by measuring its period.

The moment of inertia of the pendulum, I, is given by:

where m is the mass of the ball, M is the mass of the pendulum, T is the period of the pendulum and d is the distance from the pivot to the center of mass of the pendulum with the ball in it.

SEE BALLISTIC PENDULUM ANALYSIS

3. Find the velocity of the ball+bob immediately after impact vf by measuring the rise of the center of mass of the ball+bob system. Do this with the catch engaged. Repeat nine times. In each case find pf, the final linear momentum, and Lf, the final angular momentum of the system. The "final" moment refers to immediately after impact.

4. Repeat step 3 with the catch disengaged.

5. Compare the values (average +/- UNC) of p, L and E initial (immediately before collision) vs final (immediately after collision) for catch engaged and catch disengaged:

II. Rotational Dynamics

1. Wrap a length of string about the axle (radius of the axle: r). Attach a mass hanger to the end of the string. Pass the string from the axle over the pulley so that when the string is fully unwound, the mass is about 0.5 m from the motion detector (which rests below in the floor).

2. Accelerate the disk-axle system by allowing the mass hanger plus an added mass (total hanging mass mH ~ 500-1000 gm) to fall starting from rest. Use the motion detector to monitor the downward motion of the hanging mass with acceleration aD. When the string is fully unwound, the hanging mass will momentarily stop and then the string will start winding in the opposite direction (decelerating the spinning system) and the hanging mass will start rising up with acceleration aU. It can be shown that the experimental value of the moment of inertia of the spinning system I is approximately given by:

where you use the absolute values of the accelerations, mH is the mass hanging and r is the radius of the axle (NOT of the disc)

4. Repeat steps 2 and 3 for two other values of mH.

Do the 3 values of Imeas agree?

5. Calculate the moment of inertia of the system Icalc from the mass and radius of the disc, the mass and radius of the axle, etc.

Do Imeas and Icalc agree?