First, write down all your measured values as you shoot the ball into the arm. Be sure to set the spring of the gun to the long-range setting.
Mass of ball "m" (grams) __________ +/- __________
Mass of arm "M" (grams) __________ +/- __________
Length of arm "L" (cm) __________ +/- __________
pivot-to-center-of-mass
Swing angle "theta" (deg) __________ +/- __________
Now, use your measurements to determine the height "H" by which the center of mass of arm-plus-ball rises:
Derive the linear velocity "v2" of the arm-plus-ball after the collision.
Compute the velocity "v1" of the ball before the collision.
STOP! Give the ball to the instructor and have him check your velocity before you continue.
The next step is to predict the distance that the ball should travel if you were to shoot it horizontally off the table so that it fall onto the floor.
Height of table "h1" (cm) __________ +/- __________
Height of barrel "h2" (cm) __________ +/- __________
above the table
Total height of barrel "H" (cm) __________ +/- __________
above the floor
Now, use your measurements to PREDICT the horizontal distance "L" that the ball ought to travel from the gun's barrel to the spot at which it hits the floor.
STOP! Show work to instructor at this point.
Now, perform the experiment. Shoot the ball three times and measure its horizontal distance each time. Compute the mean and stdev of the distance. Does your prediction agree with the actual distance?