AP Physics Lab 3

Momentum Transfer Model Lab

Katie O'Byrne

Michael O'Connell

Chris Prattos

Ryan Partain

Objective: to determine the graphical and mathematical relationship between the ratio of masses to the ratio of velocities of two carts exploding.

Our group's ratio - 4:2

Materials and diagram:

Track with stoppers

One cart without a spring (508 g)

One cart with a spring (513 g)

4 individual weights (~500 g)

Ruler

Balance

Procedure:

1) place both carts on the track without weights

2) set off the spring with a ruler until you find the position at which they hit the opposite stoppers at the same time

3) Record your starting position (ours was 71 cm)

4) Find and record the displacement between starting and ending position for each cart and find the ratios of cart A's displacement to cart B's displacement (d1,d2)

5) Put one weight on cart A for a ratio of 2:1

6) Repeat Steps 2-4

7) Use additional weights to attain the following approximate ratios of the carts masses while(3:1, 3:2, 4:1, 4:2 and 4:3) , and repeat steps 2-4 for each

         Note~ when attaining the ratios, the masses may not be exactly 2:1, 3:1, ect, find the exact ratios of the masses and record them in the Data Table

8) find the inverses of your previous ratios so as to attain 1:2, 1:3, 2:3, etc. and record the data

Data Analysis:

Conclusion:    

    When we first graphed the data, it formed an inversely proportional relationship. As the mass of the carts increased, the displacement of the carts decreased. in order to linearize the data we took the inverse of the x-axis or mass values. This created a linear line of  which we were able to find the slope. This gave us the equation d1/d2= (0.72) M2/M1. However displacement  can be rewritten as velocity (V1/V2) for both carts traveled their distances in the same amount of time. Also, because one cart’s displacement was negative for it moved in a negative direction the equation must be V1/V2= (-0.72) M2/M1. The slope in this equation represents the amount in which the momentum of the two carts changed when the mass increased.

    In this lab, the data for each ratio came from a different group in the class. This left room for some errors such as each group’s track was a different length, thereby changing the starting and stopping points of the carts. We also could have hit the button that released the spring differently each time, either from an angle or with different force. Repeated trials could have loosened the stoppers by being repeatedly hit by the carts that could lead to slight errors in the displacement measurements.  One more possible source of error could be from slight variations in the starting points of the cars.  It looked the same to the human eye, but it is possible that the starting position changed a little each time we hit the cars.