The Acceleration of Gravity
The objective is to measure the acceleration of gravity ( g ) by measuring the acceleration of a falling object.
A spark generator, a few meters of spark sensitive tape, a Metric ruler, masking tape, a small and heavy weight, and a calculator
The Earth gravity exerts a measurable force on every object in its vicinity. This force is proportional to the mass of the object. The proportionality constant is the acceleration of gravity "g = 9.8m/s2 " that is to be verified in this experiment. The gravity acceleration g varies with elevation from the Earth surface; however, within a few thousand feet above the Earth's surface, it remains fairly constant. For an object undergoing a constant acceleration in the vertical direction (free fall), the following equations may be applied:
g = (Vf - Vi) /t and g = (Vf2 - Vi2)/2y where y = displacement,
Vi = initial velocity, Vf = final velocity, t = time, and g = acceleration.
Your lab instructor will demonstrate the use of the spark timer and the spark sensitive paper. This is essentially allowing a strip of spark sensitive paper to fall freely in between the spark gap of a spark generator that sparks at a rate of 60.0 per second. Each group of students should make a data tape and let it fall freely in the spark gap to obtain a set of dots. The tape will have a line of dots (caused by the sparks) on it with increasing distances between subsequent dots. The acceleration of gravity g can then be found by distance measurements in between selected dots.
As soon as you get the tape, circle the points and number them as shown in Fig. 1.
Note that the time interval from any dot to the next is 1/60 of a second. For example, the time it takes for the tape to travel from Point 1 to Point 5 is 4/60 of a second because there are only 4 time intervals in between.
Method I: Using g = (Vf - Vi ) /t .
Vi may be calculated at a point like Point 3 near the beginning of the tape, and Vf at a point like Point 3' toward the end of the tape. 3' should be read "three prime." The difference Vf - Vi divided by the corresponding elapsed time t from 3 to 3' will give us the falling acceleration of the tape or simply the g value.
1) Select a set of 5 dots near the beginning of the tape and label them as 1, 3, and 5 as shown. Ignore the very first few points that are so close to each other. Measure the initial distance, Yi, between dots 1 and 5. You may use a clear plastic ruler to measure, and convert your measurement from cm or mm to meters.
2) Select a set of 5 dots near the end of the tape and label them as 1', 3', and 5' as shown. Measure the final distance, Yf, between dots 1' and 5'. You may use the same clear plastic ruler to measure, and convert your measurement from cm or mm to meters.
3) The falling time from each dot to the next on the tape is 1/60 of a second. Initial and final speeds can be now calculated by dividing each of Yi and Yf that you measured by their corresponding travel time that is (4/60)s, that is,
Vi = Yi /(4/60)s & Vf = Yf /(4/60)s.
Vi is the average speed within Yi and is the exact speed of Point 3 within Yi. Similarly, Vf is the velocity of the tape at Point 3' within Yf .
4) The acceleration, g, can be found from g = (Vf -Vi )/t where t is the time interval between where Vf and Vi occur. It is simply the number of time intervals between points 3 at the beginning and Point 3' at the end of the tape. You need to count the number of spaces between 3 and 3' and multiply it by (1/60)s. Name the g value from this method as "gI."
The value of acceleration calculated in the above method should be close to the accepted value of g = 9.81 m/s2.
Method II: Using g = (Vfy2 - Viy2) /2y
5) The values of Vi and Vf, as found in Method A should be used. Here, y is the distance between 3 and 3' on the tape. You need a meter stick to measure it. The 30-cm plastic ruler may not be long enough. Measure y and use it in the above equation to solve for g again. You should get a similar result. Name the g value from this method as "gII."
6) Find the average of gI and gII and that will be your group measurement of g. g = (gI + gII ) / 2.
7) Calculate a percent error using an accepted value of g = 9.81m/s2.
8) A mean value can also be calculated for the whole class. Each group may want to write their measured value of g on the board for other groups to share and a mean value for the whole class be calculated with a corresponding % error.
Given: gaccepted = 9.81 m/s2.
Method I: Yi = .............. ; Yf = .............. ; t = ..............
Method II: y = ...............
Comparison of the results:
Provide the percent error formula used as well as the calculation of percent errors.
State your conclusions of the experiment.
Provide a discussion if necessary.