Quarter 3 Physics Project: Playground Physics (Part 3) Due
Wednesday, March 18th, 2015
Equipment:
You will need
♦ A Stopwatch
♦ A tape measure
♦ An accelerometer or accelerometer app
♦ A scale
♦ A camera
♦ A playground with a swing
♦ An elevator
♦ For the Extra Credit experiment: A Merry-Go-Round
The Project:
For this project, you will perform three separate experiments, and provide a detailed report
of your procedures and results, as well as an error analysis. Adhere to the following
instructions in your reports:
♦ The experimental reports will consist of an introduction, explaining what the experiment is
and what physical concepts it is demonstrating, a table of data, all calculations, your results,
and a detailed error analysis. Each of the questions in the experiments will be answered in
full sentences.
♦ All parts of the report are to be typed, including calculations. Consult the help menu of
your word processor for information on entering equations. On the website there is a link
to several commonly used symbols for cut-and-paste.
Each experiment in this packet has sufficiently detailed instructions. The rules for this project are as
the last one: You are on your own. You may not ask myself or any other physics teacher for help,
but you are free to discuss with others in your group and class any matters involving the
experiments. You may work in groups, but each person must have their own, unique data and
calculations. Everyone will perform every experiment
Experiment 1: Playground Physics: The Swing
In this lab you will measure the maximum acceleration on a swing and compare
this to a value arrived at through the principles of conservation of energy and
centripetal force.
Discussion
On a swing, we see a number of important physical phenomena, including simple
harmonic motion, driven harmonic motion, inertia, conversion of energy between
gravitational, potential, and kinetic, and centripetal force. In this experiment, we use
the latter two ideas to calculate an acceleration and then compare the results with the
acceleration we actually measure. At least two people are needed to carry out this lab.
They will need both a horizontal and a vertical accelerometer, or an app that performs
these functions.
Experiment 1: Period of a (person) Pendulum
Predict (not guess) the period of the swing when you are the bob. To do this, first take
whatever measurements are relevant to the problem, and then test your results. To test the
results, swing yourself up to a decent height, and then just allow yourself to swing and time
your swings to find the period. Find the percent error between your prediction and your
results and write a detailed error analysis. Show all work for predictions and measurements
Experiment 2: Energy and Acceleration
1. Person A begins swinging with the vertical accelerometer. Person B takes up a
position to the side so that he/she can see and measure the angle of the swinger’s
motion.
2. Person A on the swing keeps the vertical accelerometer pointed upwards along the
chain or rope, and will focus on reading the maximum value as he/she passes
through the bottom-most point of the swing. Record this value as amax
3.
Measure the maximum angle that the swinger moves to during the swing.
Line the straw side of the accelerometer
or phone with angle app up with the
chain. Consider the rest position to be
0º, and make necessary adjustments to
the measurement accordingly. The
angle that is indicated on the
accelerometer may be 90º minus the
angle from the vertical, depending upon
the device. The angle measured should
be recorded as well as its complement.
See Figure 1.
4. When the person on the swing gets to a
point where the observer on the ground
has a good reading on the maximum angle,
write down both the angle and the maximum
acceleration. Repeat in this manner
for at least three different angles, then change
places and repeat. Record your data in a data
table.
5. To determine the change in the height of the
swinger, use the recorded angle as shown in
figure 2 or measure directly.
Perform at least 3 trials and record all data and calculations in a clear, organized data table
Analysis
1. From your measurements and the potential and kinetic energy formulas, determine your
velocity at the bottom of the swing
2. The acceleration at the bottom of the swing has two parts: gravity and centripetal. We
can show that the centripetal acceleration is just v2/L, where L is the length of the swing.
Calculate this value and convert to g’s by dividing your result by 9.8 m/s2. Add 1g due
to gravity to get the total acceleration.
3. Compare the values you calculated and the corresponding values measured on the swing.
Examine the situation and suggest areas where your calculations could have been off due
to approximations.
Picture
4. Have your partner take a picture from the side at the moment
you have reached your maximum height. On this picture, measure
and indicate the angle of displacement from the rest position and
include this picture with your project. Calculate the force due to
gravity (Fg), force of tension (FT), and the restoring force (FR) and
draw vectors to scale for each on the picture.
FR
FT
Fg
Part 2: Elevator Physics
 The SHA elevator may not be used for this experiment, because it is too slow to yield accurate
readings. In general, the taller the building, the faster the elevators. You do not need to go to
the Empire State Building, there are plenty of buildings in the local area with sufficiently fast
elevators. In your report, indicate where the elevator is and include a picture of yourself in the
elevator with the vertical accelerometer as you are ascending or descending.
The net force on the mass in the accelerometer is given by the relationship:
F - mg = Fnet = manet
where F is the force applied to the accelerometer and mg is the weight due to gravity of the
mass. When the mass is at rest or moving with constant speed in an upward or downward
direction, the net force is zero and the net acceleration of the mass is zero.
If the accelerometer is calibrated to read “1g” when it is at rest, that recognizes the 1g effect
of gravity. To get the net acceleration of zero, you subtract 1g from the reading.
If the mass is accelerating upward at a reading greater than 1g. Again, the net acceleration
can be determined by subtracting 1g from the accelerometer reading. The reading will still
be above zero (positive) indicating an upward acceleration.
If the mass is accelerating downward, it will be above the “1g” position, or a reading of less
than 1g. Subtracting 1g will yield a negative net acceleration in agreement with the
downward acceleration of the mass.
Procedure
Hold the accelerometer stationary against the wall of the elevator and record the readings
during each of the following instances:
Standing still Beginning ascent Middle of ascent Slowing ascent Stopped Beginning descent Middle of descent Slowing descent Stopped Trial 1 Trial 2 Trial 3 This table is to be retyped with your data
for inclusion in your
project
Questions
1. Are the magnitudes of the accelerations different at the beginning of the ascent than in
the middle of the ascent? Explain why this is so.
2. How does the starting acceleration compare with the stopping acceleration? Was it the
same during the ascent as it was during the descent?
3. Were the acceleration values constant during any of the periods of acceleration, or did
they vary? How did they vary? Were they all the same pattern?
4. How did you feel in each of the situations where you took readings? Compare your
feelings with the accelerometer readings.
Analysis
From your acceleration data, create another table and determine the net force you experienced
during each portion of the trip for all three trials. Describe any additional measurements you need
to take and show all work for calculations and measurements.
Picture
Have your partner take a picture of you on the elevator while it is ascending. Make sure that both
you and the accelerometer are visible in the picture. Draw a free-body diagram to scale of the
forces on you as the elevator ascends. Show all work for calculations and measurements. Smile! 
Extra Credit: Merry-Go-Round Physics
You may use either a playground merry-go-round or an amusement park merry-go-round for this
section. The former “Nunley’s” carousel is nearby on Museum Row.
1. Measure a distance from the center of rotation. Place the lateral accelerometer at that distance,
holding it against a bar if necessary to keep it from moving, and holding it so that it is level. .
Record the distance, r, in Table 1.
Note: Several riders, each with a lateral accelerometer, could be positioned simultaneously at
different distances.
2. Push the merry-go-round at a constant speed.
3. Measure the period of rotation as accurately as possible.. make not of the method used for
finding the period and record all data
4. Record the lateral acceleration while rotating.
5. Repeat the above steps at a different radius.
Analysis: Show all work for calculations and measurements.
1. Calculate your tangential velocity on the merry-go-round.
2. Calculate your centripetal acceleration from the velocity and your other measurements
3. Compare the calculated acceleration to your measured acceleration and calculate the
percent error between them.
4. From your data, determine the relationship between radis and centripetal acceleration.
Picture
While you are on the merry-go-round, have your partner take your picture. On the picture, draw to
scale a vector representing your tangential velocity at that moment.