The Acceleration of Gravity ( g )
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
Gravity exerts a force on every object. This force is proportional to the mass of the object. The proportionality constant is the acceleration of gravity "g." The gravity acceleration (g) varies with change in elevation; however, for a few thousand feet above the Earth's surface, it remains fairly constant. For an object undergoing a constant acceleration, the following equations of motion may be applied.
(1) Vf = Vo+ a t (3) Vf 2 – Vo2 = 2 aX
(2) X = [(Vf + Vo) /2]t (4) X = Vo t + ½ at 2, where:
X = displacement, Vo = initial velocity, t = elapsed time, Vf = final velocity, and
a = acceleration. For falling objects: a = g = 9.8 m/s2 .
The 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 between the spark gap while the spark timer is sparking at a frequency of 60. sparks per second. Each group of students should obtain a data tape. The tape will have a line of dots on it separated by increasing distances between subsequent dots. The acceleration of falling motion can then be found by using the following methods:
As soon as you get the tape, circle the points and number them as shown in Fig. 1.
Find the acceleration by using the equation g = ( Vf – Vo ) /t .
Vo may be calculated at a point near the beginning of the tape, and Vf at a point toward the end of the tape. The difference (Vf-Vi) divided by the corresponding elapsed time ( t ) will give the acceleration of the tape:
g = (Vf – Vo) / t .
Measure an initial distance, Xo, between 5 dots at the beginning of the tape and a final distance, Xf, between 5 dots toward the end of the tape. It is better to ignore the first few points that are very close to each other, because the relative error in measuring a small distance is high. Also, the last few points that may not be along a straight line should be disregarded.
Calculate the initial and final velocities using the distances traveled ( Xo and Xf ) and the travel time for each of (4/60)s, that is,
Vo = Xo / (4s/60) & Vf = Xf / (4s/60).
Since the time interval between every two neighboring dots is 1/60 sec (the spark timer produces 60 sparks per second), the time interval corresponding to each of Xo or Xf is therefore, (4/60)s.
Vo is the average velocity within Xo and is the velocity of the 3rd point within Xo. Similarly, Vf is the velocity of the tape at the 3rd point within Xf .
The acceleration, g, can be found from g = ( Vf – Vo ) / t, where t is the time interval between Vf and Vo . It is the number of time intervals between points 3 at the beginning and 3 at the end, in Fig. 1.
The value of acceleration calculated in the above method should be close to the accepted value of g = 9.8 m/sec2. Calculate a percent error.
Find the acceleration g, by using the equations: Vf2 – V02 = 2gX & X = Vot + 1/2 g t2 .
Values of Vo and Vf, as determined by Method A should be used. Obtain any necessary measurements and calculate “g” again using each equation. You should get similar results. Calculate a percent error for each case using the %error formula shown:
Given: gaccepted = 9.8 m/s2.
Method A: Xo = ………, Xf = ………, t = ………..
Method B: Vo = ………, Vf = ………, t = ………., X = .............
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.