__Experiment 4__

**
The Acceleration of Gravity ( g )**

__
Objective:__

The objective is to measure the acceleration of
gravity ( g ) by measuring the acceleration of a falling object**.**

__Equipment:__

A spark generator, a few meters of spark sensitive tape, a Metric ruler, masking tape, a small and heavy weight, and a calculator

__Theory:__

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) V_{f} = V_{o}+ a**
**t
(3) V_{f }^{2} – V_{o}^{2}
= 2 aX

(2) X =
[(V_{f}^{ } + V_{o})
/2]t
(4) X = V_{o
}t +
½ **
a**t^{
2}, where:

**X =** displacement, **V**_{o}** =** initial
velocity, **t
=** elapsed time, **V _{f} =**
final velocity, and

**
a**
= acceleration. For falling objects: a = g =**
9.8 m/s ^{2} .**

__
Procedure: __

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**.

**
Method A:**

Find the acceleration by using the equation **g** = ( V_{f} – V_{o}
) /_{t}
**.**

V_{o}
may be calculated at a point near the beginning of the tape, and V_{f}
at a point toward the end of the tape**.** The difference (V_{f}-V_{i}) divided by the corresponding elapsed time
( t ) will give the
acceleration of the tape**: **

**g**
= (V_{f} – V_{o}) / t
**.**

Measure an initial distance, X_{o},
between 5 dots at the beginning of the tape and a final distance, X_{f},
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 ( X_{o} and X_{f} ) and the travel
time for each of (4/60)s, that is,

V_{o }= X_{o }/
(4s/60) & V_{f } = X_{f }/ (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 X_{o}
or X_{f
}is therefore, (4/60)s.

V_{o}
is the average velocity within X_{o} and is the
velocity of the 3^{rd} point within X_{o}**.** Similarly, V_{f}
is the velocity of the tape at the 3^{rd} point within X_{f} **.**

The acceleration, **g**, can be found from **g = ( V _{f} – V_{o
}) **

The value of acceleration calculated in the above method should be close to the
accepted value of **g = 9.8 m/sec ^{2}**.
Calculate a percent error.

**
Method B:**

Find the acceleration **g**, by using the equations**:** V_{f}^{2}
– V_{0}^{2} = 2**g**X & X = V_{o}t
+ 1/2** g** t^{2} **.**

Values of V_{o} and V_{f}, 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:

.

__
Data: __

**
Given: **
g_{accepted}
= 9**.**8 m/s^{2}.

**
Measured**:

Method A**: **X_{o}
= ………, X_{f} = ………, t = ………..

Method B**: **V_{o}
= ………, V_{f} = ………, t = ………., X = .............

__
Calculation(s):__

__
Comparison of the results:__

Provide the percent error formula used as well as the calculation of percent errors.

__
Conclusion:__

State your conclusions of the experiment.

__
Discussion:__

Provide a discussion if necessary.