Description
the professor says “Just email me the results when you have completed them. You will haveplots and numbers from the experiments so you might want to put theplots and numbers in a document and just email me the pdf of the file.There is no need for a full write up (no need for an introduction ormethodology) just the results (plots and numbers as stated in the labmanual sections).” and here are 3 experimant. 1 and 2 has an Excel with it, but I couldn’t upload it in here [email protected] email me Hi to send you the excel via email
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3. Simple Pendulum
3.1
Introduction
This lab studies the behavior of a classical periodic motion, the simple pendulum. The simple
pendulum exhibits periodic motion. When the angle of oscillation is small, the motion is “simple
harmonic”.
For this experiment you will perform a virtual online experiment to look at the periodic motion of a
pendulum. In particle, there are a couple of online sources for this:
1. Online virtual experiment using the PHET Pendulum Interactive Simulation.
2. Online virtual experiment using a HTML5 app provided by Walter Fendt.
3.2
Procedure
You have to obtain the period of the oscillation as a function of the length of the string, and the
mass at the end of the string.
The two different virtual online experiments are provided in case one doesn’t work, or in case you
have a preference. Use whichever you like. In the end, you just need about 10 data points for the
period as a function of length, and about 10 data points for period as a function of mass (so around
20 data points in total).
3.2.1
PHET Pendulum Interactive Simulation
1. Keep the mass fixed (the default of 1 kg is fine). Make the length as small as it will go (0.1 m)
and click and drag the mass to release it and set it oscillating back and forth.
It moves pretty quickly, so measuring the time of one period (time to move forward and back again)
is too small to accurately measure. Therefore, measure 10 periods, and divided the number by 10
Week 3. Simple Pendulum
14
(move the decimal point to the left) to obtain the period. There is also the option to slow it down, as
this is a simulation (something that we obviously can’t do in real life).
2. Increasing the length (you want around 10 data points all together). And measure the new period.
Repeat until you have 10 periods (in seconds) for 10 lengths (in meters).
3. Now keep the length fixed (somewhere in the middle is fine).
4. Vary the mass to obtain 10 times for the 10 different masses. Again, measure 10 periods, and
divided the number by 10 (move the decimal point to the left) to obtain the period.
3.2.2
HTML5 app provided by Walter Fendt
The same procedure can be followed as previously. The two main differences with this virtual
online experiment is that you have to stop the experiment (not just pause) before changing the
values of either the length or mass. Also, while measuring the period makes sense in terms of
imagining recording the experiment (say with a stop watch), this simulation displays the oscillation
period.
Again, the objecting to to obtain 10 periods for 10 different lengths (when mass is constant), and 10
different periods for 10 different masses (for when length is constant).
3.3
Analysis
We will assume that the period of the oscillation is of the form
T = kLm M n
where T is the period, L is the length of the string, M is the mass of the bob, and k, m, and n are
constants to be determined.
Week 3. Simple Pendulum
15
• Plot log(T) as a function of log(L) and obtain the slope m.
• Plot log(T) as a function of log(M) and obtain the slope n.
• Plot T versus Lm M n to obtain the constant k.
Write down a form of the equation with numbers in it.
You will upload your plots and your equation to the weeks discussion board.
3.4
Discussion
Does your functional form match the equations obtained by everyone else in the class? What’s up
with mass?
6. Physics of Walking
6.1
Introduction
Here we’ll explore the physics of walking. Physicists have developed several simple models to
describe walking. Bellemans (Am J Phys 49, 25-27, 1981) created a model that described the
relationship between walking speed (v), stride length (d), and leg length (L) through the optimization
of power expenditure. Lin (Am J Phys 46, 15-18, 1978) described a different model that produced
a similar relationship.
Lin’s model presumes that one walks by letting one leg swing forward freely, transferring weight to
it, and repeating the process with the other leg. The swinging motion is that of a simple pendulum
and we use this to calculate the speed of walking.
vwalk =
d
t
where d is the length of a stride and t is the time of the stride. If we assume the leg is a simple
pendulum of length L/2 where L is the length of the leg and the center of mass is assumed to be
half away down the leg (is this reasonable?). The period T is of course
s
L
T = 2π
2g
where g is graviational acceleration (this is why it is hard to walk on the moon and astranauts had
to bounce around). The time of stride is half of this and so the theory might predict that the velocity
is of the form
√
2g d
√
vwalk =
π
L
and velocity increases with stride length, but decreases with leg length.
Week 6. Physics of Walking
6.2
26
Procedure
For this experiment you will be analyzing data that has been obtained for you. In particular, the
data can be found in the spreadsheet “experiment6.ods”. This data is from a paper publushed in
Young, C., Young, K., Buxton, G., & Buzzelli, A. (2017). Field day at the rec: working out with
physics. The Physics Teacher, 55(3), 155-158.
6.3
Analysis
We will explore the model
√
2g d
√
vwalk =
π
L
• plot log(vwalk ) vs d and obtain a straight line fit. What is the slope?
• plot log(vwalk ) vs L and obtain a straight line fit. What is the slope?
• plot vwalk as a function of √dL . Does it appear linear? What is the slope? What is the intercept?
Do you recover the acceleration due to gravity from your data?
You should upload the plots of the data, and the value you obtained for g.
6.4
Discussion
Does the data agree with the physics model? Two sets of data predict similar relationships, but they
are not quantitatively the same.
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