Name: _____________________ Class: Physics 214
SSN/ID:   _____________________ Section & Group: ____________
Lab 3 - Gravity

Objective
To determine the acceleration of gravity acting on a freely falling object.

Equipment
URL: http://ippex.pppl.gov/interactive/matter/freefall.html

Definition
The idea in this lab is to determine the acceleration due to gravity and to see if it truly is 9.8m/s2. The acceleration due to gravity is symbolized by the letter g (Note: the letter g does NOT stand for grams!) and is measured in units of m/s2, or: 

     [meters]
------------------
[second · second]
The way you'll calculate this acceleration due to gravity is to first determine the velocity at two different points. Remember, the velocity, in this case, is just the speed of the particle at two different points. Speed is simply the: 

                       [change_in_distance]
speed (or velocity) = ----------------------
                         [change_in_time]
and is symbolized by: v = Δd/Δt. Acceleration, on the other hand, is simply the change in speed (either the increase or decrease): 

                [change_in_velocity]
acceleration = ----------------------,
                  [change_in_time]
is symbolized by: a = Δv/Δt, and is measured in units of m/s2.

Procedure

  1. Change the following applet settings (these are the items marked with a star & a number in the figure below):
    1. Set Distance multiplier to 1
    2. Set Velocity multiplier to 0
    3. Set Acceleration multiplier to 1
    4. Change Height to 20
    5. Change Air Density to 0
    6. Change delta-T to 0.10sec
    7. Set Time to 3 (sec)
    8. Change -10 to 0
  2. Now release the ball by clicking the Release Ball button
  3. Record the height and time measurements for 10 consecutive dots on the table below. Ignore the first couple of dots (when it started to move through the timer) and the last one (when it hit the ground).
    • Move the mouse pointer over the points on the graph to display the (x,y) coordinates
    • The x-coordinate is the time (in secs) and the y-coordinate represents the distance, or height, in meters
    • For example, in the figure above, the box with the red arrow shows that its x-coordinate is the time (1.10 secs) and its y-coordinate is the height (6.70m). If you move the cross-hair cursor over the points, it'll display their x- and y-coordinates.
      • In order to calculate Δd, you need to use the formula: 
        Δd = dfinal - dinitial
        In this case, to calculate Δd for the time 1.10 secs, you need to use this formula as follows: 
        Δd = d1.10secs - d1.00secs	    	    
Δd = 6.70m - 5.10m = 1.60m
        Basically, the idea is to use the PRIOR VALUE for distance/height as the initial value and the current value for distance/height as the final value.
  4. Now repeat the above for a mass of 0.50-kg by changing the mass slider (don't forget to click the Clear Trails button!).
  5. Record this data in the table below, too.
  6. Now calculate the speed between the points on the data table by dividing the change in distance (in meters) between the points by the time interval between the points (0.10-sec): 
    
                 Δdab                     Δdab = db - da
Velocity vb = ----------     where -----------------------------
                 Δtab               Δtab = tb - ta = 0.10-sec
    Remember: the velocity is the average velocity at the end time.
  7. Plot the change in speed vs. time. The slope of that line is the acceleration due to gravity.
    • Calculate the slope of that line by dividing the change in velocity from the first interval to the last interval by the change in time between those intervals: 
      
          rise       Δv12      v2 - v1
Slope  = ------  = ------- = ----------     where Δt12 = t2 - t1
           run       Δt12        Δt12
      Remember: the slope = acceleration due to gravity!
  8. Compare your measurement of the acceleration due to gravity with the known value for g (9.8 m/s2) by calculating the percent difference: 
    
                   (Acceleration_Expected - Acceleration_Measured)
    % difference = -----------------------------------------------   x 100
                                Acceleration_Expected

Questions

  1. Compare the two plots for the two objects of different mass. Explain any differences.

Notes

  1. The acceleration due to gravity, g = 9.8 m/s2

























Time Position Coordinate Ball Mass = 0.05-kg Ball Mass = 0.50-kg
Δdover the interval vend of interval Δdover the interval vend of interval
0.10-sec        
0.20-sec        
0.30-sec        
0.40-sec        
0.50-sec        
0.60-sec        
0.70-sec        
0.80-sec        
0.90-sec        
1.00-sec        


Graph of v vs. t