Lab 1: Acceleration of Gravity

Purpose: The purpose of this lab is to determine the acceleration of gravity for a freely falling object. And to gain experience using the computer equipment to collect data.


Equipment: 

• Lab Pro interface

• Logger Pro software

• motion detector

• rubber ball

• wire basket

Introduction: In this laboratory you will use the computer to collect some position (x) vs time (t) data for a rubber ball tossed into the air. Since the velocity of an object is equal to the slope of the x vs t curve, the computer can also construct the graph of v vs t by calculating the slope of x vs t at each point in time. We will use both the x vs t graph and the v vs t graph to find the free fall acceleration of the ball.

Procedure: For this lab we first logged into Logger Pro to get a blank position vs. time graph. We had our position axes range from 0 to 4 (m), and our time axes range from 0 to 4 (s). We then hooked up our motion detector to Lab Pro interface, placed it on the floor and and put the wire basket above it, making sure that the wires of the basket weren't directly on top of the motion detector. While one member tossed the rubber ball up from about 1 m above the detector,  another member would  "collect" the data. The toss should have the ball going up then down directly above the detector for a more precise reading. We ran 3 trials, and for each of these trials we tried to get our position-time graph to be a parabolic shape since it would show the effect of gravity pulling the ball down when its tossed. After we had our data collected, we did a curve fit for the position vs. time graph for each trial to get an equation that would interpret the balls motion. 

Position-time graph

We used the quadratic fit (at^2 + bt + c) for our parabolic graph, equation , which gave us our values for a, b, and c. We used unit analysis to find the acceleration of our g exp for each trial. This was done by multiplying 2 to our a value given in our curve fit. We then calculated our percent difference percent to check how far off we were from getting the accepted value of gravity which is -9.8 m/s^2.

Velocity-time graph

After doing our curve fit we took a look at our velocity-time graph for the motion of our ball. We did a linear fit for this graph since we took the derivative of our position-time graph which gave us a linear graph for our velocity. The slope (m) of our graph gave us a close or equal measurement of -9.8 since the change in our velocity equals acceleration. Our acceleration of gravity came out as a negative value since the computer program read anything above our motion detector to be the positive direction and anything going down as our negative direction, and zero would be the position where our ball stopped going up and started to fall. Once we got our slope we calculated our percent difference.

Conclusion: In this lab we tracked the movement of a falling ball to solve for the acceleration of gravity. We  learned to read our position vs. time and velocity vs. time graphs. I also learn that for position graphs we are going to be given a parabolic graph since it shows the motion of our ball, while the velocity graph will be linear since the object in motion is uniform. Our results came really close to being exactly -9.8m/s^2. A source of error could be human error, as well as our motion detector recording outside interference which could have hampered our data since our ball wouldn't always land right on top of our motion detector.