Physics 1020
NAME ________________________
Laboratory 3: Acceleration due to gravity
Prelab: Please do this prelab before you read the lab writeup.
In Laboratory 1 you made use of the value of g, the acceleration due to gravity at the
surface of the earth, to measure human reaction times. Discuss two possible ways of measuring
g. (There are many ways of doing so.)
Why is knowing the value of “g” important in our everyday lives? (list two reasons)
Now read the rest of the lab before showing up to lab.
Group Names:
Laboratory 3: Acceleration due to gravity
In this laboratory we will measure g in two ways: (1) Timing the swing of a pendulum and (2)
Measuring the time it takes an object to fall a known distance.
1. Simple Pendulum
A simple pendulum consists of a weight attached to a wire or string, hanging from a point
where the string is attached (See the figure. )
Θ
L
1. Setting Up the Pendulum
a) First, get acquainted with the pendulum equipment. Examine the apparatus. A string
hangs from a point. You can attach different weights to the end of the string. Length
of the string can be adjusted with two knobs on top of the apparatus.
b) Your measuring equipment includes a protractor to measure the string angle. a meter
stick to measure the pendulum length, and a scale to measure the mass of the
weights.
c) Get some practice with the equipment, as follows. You don't have to write anything
down.
1. Find the mass of one weight. Place the weight on the hook at the end of the string.
2. Adjust the string to a height of your choice. Measure the pendulum length. To do
this, measure from the point to which the string is attached at the top to the middle of
the weight at the bottom. (We want to measure to the “center of mass" of the weight.
The middle is a good approximation of this.)
3. Have one person center the protractor at the top of the string, while another person
GENTLY moves the weight a small amount (about 5o) to the left or right of vertical.
The person with the protractor should measure the angle (vertical is 0o).
4. Release the pendulum from this small angle. Do NOT give the pendulum a push -just open your hand and let it go. The point of the lab is to observe smooth, steady,
controlled motion as the pendulum swings back and forth through a small angle.
5. In the next section you will repeat this procedure over and over, so make sure you
understand how to measure the mass, length and angle, and how to start the pendulum
motion. Ask your TA if you have any questions.
2. Measuring the period of the pendulum
The goal is to vary experimental conditions while repeatedly measuring the period of the
motion of the pendulum. In each case you will change the mass or the pendulum length and
then measure the period.
What does “the period” mean? You will have noticed that the pendulum swings back and forth,
executing the same motion over and over. Anything that repeats the same motion over and over
is said to oscillate. We might ask, “How long does it take to complete one full cycle?” The
answer is called the period of the motion. For a pendulum, the period is the time it takes the
pendulum to go from its furthest point right, to its furthest point left, and back to its furthest
point right again. You can also measure the period starting at any other point in the motion, as
long as you begin and end the measurement with the pendulum at the same point and moving in
the same direction. Be careful not to measure half a period by mistake!
A NOTE ABOUT TAKING DATA: The most important experimental technique (besides
safety) is accurately and honestly reporting the data you take. Even if you think you know what
answer you should get, don't fudge the data to get that answer. You are being graded on good
experimental technique, not on having perfect data!
2.1 Varying length (use the table on the next page)
In this part of the lab you will take data to find out how the pendulum period changes when
string length changes. All other variables must be held constant. Use a reasonable number of
significant figures when recording data.
1. Select a weight and a starting angle of 10o or less. Record both in the data table provided.
You will use the same weight and angle for this entire part of the experiment.
2. Measure the pendulum period (as described below) with three different string lengths of
your choosing. Use a nice range of lengths û from 10 or 20 cm up to more than a meter.
3. Measuring period:
a. Let the pendulum go and measure the time it takes the pendulum to swing ten full
cycles. Then divide the measured time by ten to obtain the period. This is one trial.
b. Repeat the cycle without changing anything to obtain 3 trials for each string length.
Average your results and record everything in the data table provided.
4. Does the value of the period depend on the length?
Data Table for 2.1 Varying Length
Mass
Angle
Length
Period (3
trials)
Period (ave.)
Uncertainty
2.2 Varying mass
1. Repeat the steps from the previous section, but this time pick three different masses. Keep
the pendulum length and the starting angle fixed. Record the data in the table provided.
2. Does the value of the period depend on the mass?
Data Table for 2.2 Varying Mass
Mass
Angle
Length
Period (3
trials)
Period (ave.)
Uncertainty
2. Finding the acceleration of gravity with the pendulum. The correct formula for the period
is written below. Does the period depend on length, mass and/or angle?
p
T = 2⇡ L/g
How does the formula compare to your conclusions from the last section? Did you correctly
determine what the period depends on? (Be honest -- you will not be penalized for getting it
wrong as long as you showed good technique.)
Use the above formula with three of your measured values of the period and other variables, to
determine g, the acceleration of gravity, from this formula. Average the three estimates together
to get your final prediction. How does it compare with the accepted value?
Length
Time (ave)
g
Uncertainty
3. Explain briefly how you estimated the uncertainty in g.
3. Dropping the Ball
The final section of the lab uses a different apparatus to measure the acceleration of gravity.
Here, you will drop a ball from three different heights, and measure the time it takes to fall.
The setup is simple -- an electromagnet holds the ball in place at the top. Pushing a button
releases the ball, and a photogate below records the time the ball took to drop.
Measure each of the three heights carefully. Be sure to measure the correct length -- think
about which part of the ball the photogate sees first.
For each height, do three trials of the ball-drop. Let the ball drop and record the time in the
table provided. For each height, average the four trials and record the data.
Height vs. Time for Ball Drop
Recall from Laboratory 1 that for an object falling under the influence of gravity
d = ½ g t2
or g = 2 d/t2
Record your data for the falling bodies and calculate g using the average time and estimate the
uncertainty in g.
Height
Time
Average Time
g
Uncertainty in g
.If time permits, plot the height versus time, and also the height vs. (time)2. (Graph paper is
on the next page and your x-axis should have two different sets of labels.) Which graph is
linear? Discuss what this implies?