Lab #4 - the Ballistic Pendulum

Lab #6 - The Ballistic Pendulum Name: ______Copyright R. Mahoney 2014

The purpose of this lab is to use conservation of linear momentum and mechanical energy to determine the initial speed of a ball shot out of a spring-loaded "gun" (but caught in a cage almost immediately). We then independently determine that same speed by 1) measuring the vertical drop and horizontal range of the ball when shot horizontally out of the same "gun" but allowed to fly freely to the floor below, and 2) using constant acceleration (kinematic) formulae.

Answer all the interspersed questions (Q) at the end of the lab (back of page 2).

All formulae will be explained in class.

For convenience and space requirements, half the groups should do Part 2 first.

Part 1: Catching the Ball

You will be shown in class how to cock the ball consistently. We will be cocking the ball to stage three for all shots. The ball should be placed at the back of the shooting tube, not at the front (as shown on the gun itself). Using the plumb line attached to the "gun", make sure that it is horizontal. Set the plastic angle deflection marker to zero degrees. If it has a zero error, make a note of that error, and subtract or add it to your angle deflection readings as necessary. As shown in class, use the torque experiment fulcrum to find the center of mass of the pendulum (with the ball inserted, but the affixing thumbscrew not inserted).

Make the following preliminary measurements:

Zero error of plastic angle deflector: ______deg

Mass of ball (m): ______kg Mass of pendulum (M): ______kg

Length of pendulum from axis of rotation to center of mass of pendulum when ball captured in cage (L): ______m

With the ballistic pendulum fully assembled and clamped to table side, shoot the ball 5 times, and write down the angles of deflection (in degrees):

______

What is the average deflection angle (θ) in degrees? Answer: _____

Determine the "raise height" (h) of the ball plus cage after collision: h = L (1 - cosθ) = ______m Using g = 9.804 m/ sec2, calculate the initial speed (v) of the ball when shot from the gun, using the following formula: v = [(m + M)/m] [2gh]½ Answer: ______m / sec

Q1: Give two non-trivial systematic errors for part one of this experiment.

Part 2: Shooting the Ball

Remove the pendulum from the apparatus. In shooting the ball, make sure that it is cocked to stage 3. Make trial shots as necessary to determine range. The apparatus should be clamped to table side. Tape a white sheet of paper (with carbon paper on top) so that the target paper does not move when a ball hits it, but a mark is left where the ball landed. Make sure that when you shoot the ball, you don't inadvertently hit someone. Your "gun should be "square" to the table (lined up in a fashion parallel to a table edge).

Use a plumb line to measure the vertical distance (H) that the bottom of the ball drops. Alternatively, use one of the tape measures available in class (tape measures are in inches, so you would need to convert to meters).

H = ______m

Q2: Why do you use the bottom of the ball when determining H?

Make five shots and measure the horizontal range (R) for each shot (distance from plumb point to where ball hits). Use the floor tiles for "square alignment" as necessary. Again, you can use a string, a tape measure, or a meter stick to measure each value of R.

______(all in m)

Average range R = ______m

Q3: At what location does the ball's horizontal journey begin? Did you plumb from this position?

Using g = 9.8 m/ sec2, calculate the initial speed (v) of the ball when shot from the gun, using the following formula: v = R (g /2H)½ Answer: ______m / sec

Compute the percent difference between the two values of v.

Answer: ______%

Q4: Give two non-trivial systematic errors for part two of this experiment.