Experiment 4

**The Acceleration of Gravity**

__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__:

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/s*^{2} " 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 ***=
(V**_{f} - V_{i})_{ }
/t**
and ***g ***=
(V**_{f}^{2} - V_{i}^{2})/**2y**
where *y* = displacement,

*V*_{i} = initial
velocity, **V**_{f
}= final
velocity, **t **= time,
and **g** =
acceleration**.**

__Procedure__:

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**.

Figure 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**** ****=
(V**_{f} - V_{i}
) /t .

**V**_{i} may
be calculated at a point like **Point 3** near the beginning of the tape, and
**V**_{f} at
a point like **Point 3'** toward the end of the tape**.** *
***3' **should be read "**three prime.**" The difference** V**_{f
}**- V**_{i } 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, Y**_{i},
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, Y**_{f},
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*. *I***nitial and final
speeds **can be now calculated by dividing each of *Y*_{i} and
**Y**_{f} that
you measured by their corresponding travel time that is (**4****/****60**)**s**,
that is,

** V**_{i }=
Y_{i }**/****(4****/****60)s
& V**_{f }=
Y_{f }**/****(4****/****60)s****.**

**V**_{i} is
the average speed within **Y**_{i} and
is the exact speed of **Point 3** within Y_{i}**.**
**Similarly, V**_{f} is
the velocity of the tape at **Point 3'**
within Y_{f} **.**

**4) **The acceleration, **g**,
can be found from *g*
= (V_{f} -**V**_{i })**/t**
where **t** is
the time interval between where **V**_{f} and **V**_{i} 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 "*g*_{I}."

The value of acceleration calculated in the above
method should be close to the accepted value of **g
= 9.81 m/s**^{2}.

**Method II:** **
Using ** *g ***
=**
(**V**_{fy}^{2} -
**V**_{iy}^{2})
**/2y**

**5)** The values of **V**_{i} and
**V**_{f}, 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 "*g*_{II}."

**6)** Find the average of
*g*_{I} and
*g*_{II}
and that will be your group measurement of *g*.
*g = *(**g**_{I}
+ g_{II} )** /
2.**

**7)** Calculate a percent error using an **
accepted value of** **g = 9.81m****/s**^{2}.

.

**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**.**

__Data__:

** Given: ** ** ****g**_{accepted} **=
9.81 m****/****s**^{2}.

**
Measured:**

* Method I: * Y_{i} =
.............. ; Y_{f} =
.............. ; t = ..............

*
Method II:* y = ...............

__Calculations__:

###
Provide the necessary calculations**.**

__
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**.**