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Acceleration of Gravity

Safety: Wear goggles during the experiment to prevent physical damage to eyes. The danger is due to people working around you in addition to your experiment. Wear goggles until you are away from the lab area.

Procedure Part A:

The picture to the left shows how the gravity drop is set up.  Observe that the red cable is attached to the top photogate and the blue cable is attached to the bottom photogate.
  
Observe that the red cable is plugged into the A channel and the blue cable is plugged into the B channel.

Since the A light and B light are both lit, the time displayed is the time for the marble to pass from A to B.  In our setup, it is the time to pass from the top photogate to the bottom photogate.

Setup gravity drop apparatus with photogates approximately 5 cm apart measured to the nearest 0.1 cm. Measure this distance from the middle of one eye to the middle of the other eye. Also measure distance from bottom of ball to the middle of the top photogate eye. Set timer on interval. Release ball and record the time. Repeat at the same settings.

Move the release mechanism further down the stand making the same measurements.

Continue until you have the time interval at 6 different distances.

Repeat using the other type of marble.

Calculations:

Use the average time interval for each displacement.

Calculate the average velocity at each displacement. The displacement used to calculate the average velocity is the distance between the photogates.

The displacement used to calculate the acceleration is the distance from the bottom of ball at rest to the mid point between the photo gates. The initial velocity and initial displacement are 0.

               v2 - vo2
x = xo + ------------
                  2a

solve for acceleration at each placement. xo and vo are both 0.

Calculate average acceleration, standard deviation, and percent standard deviation.

Calculate the Percent Error in the average acceleration. The theoretical value is 9.80 m s -2.

    

Procedure Part B:

    
The picture above shows the original picture.  The strobe was flashing 3000 times a minute or 50. times a second.
   
The picture above was first converted into black and white.  Next, it was turned into a negative.  The stand is 1.01 meters tall.

   
Measure the length of the stand in centimeters.

Write equality         measured length stand  cm  =  1.01 meters

Measure the distance between consecutive dots.  Ignore dots that are too close together to properly measure.  

Use the above equality to convert to the actual distance between the dots.

Average velocity between consecutive dots = distance / 0.020 seconds

Graph average velocity vs total time.

Slope of the line is the experimental acceleration of gravity.

Calculate the percent error in the acceleration of gravity.   The theoretical value is 9.80 m s -2.