Lab #2 - Super Heroic Physics: Mr. Fantastic

Rodney Garland

PLAB 223-01

11/23/11

Introduction -

Have you ever had trouble starting an assignment because of a lack of ideas? This has been a problem of mine for a very long time, even going back to an early college English class where I resorted to writing an essay about writing an essay. I went through a lot of ideas and I finally decided on the following.

The best solution to beating writer's block is to go back to the basics. What are you interested in? Why are you interested in it? And, how do you want to convey this interest to your professor and relate it to the topic at hand? My interests lie in things such as: video games, professional wrestling, psychology, mathematics, and, perhaps the most important to this upcoming discussion, superheroes. With this in mind, I've taken those interests to heart and applied what I know to bring up questions and reach conclusions. Do you know what that sounds like? The perfect lead-in to a lab report.

This report will cover the ideas of elasticity and tension. The example we will use to convey these ideas will be none other than Marvel comic book character, Mr. Fantastic.

Procedure -

The first step was to gather the supplies: five 33 size elastic rubber bands, one LeverLock 16 foot tape measure, safety gloves, and, of course, safety goggles. Lining up one end of a rubber band to the start of the tape measure, we began stretching the rubber band horizontally, while recording it's length. The rubber band would continue to be stretched, at room temperature, until it snapped, the final length being recorded as the breaking point. From there, four more rubber bands were put through the same test. After all five rubber bands reached their breaking point, the data was recorded and then averaged.

Data Collection -

Uniform Mass: 4.56g

                                      Starting Length               Breaking Point               Stretched Distance

Rubber Band #1 -                  5.5in.                             26in.                                20.5in. (.52m)

Rubber Band #2 -                  5.6in.                             26.2in.                             20.6in. (.52m)

Rubber Band #3 -                  5.4in.                             26.6in.                             21.2in. (.54m)

Rubber Band #4 -                  5.5in.                             26.5in.                             21in.    (.53m)

Rubber Band #5 -                  5.6in.                             27.4in.                             21.8in. (.55m)

Average Stretched Distance:  21.02in. (.53m)

Data Modeling -

So, how do we relate this rubber band to Mr. Fantastic? Well, we found out how far these rubber bands can stretch before reaching their breaking point. Now, we can ask a question. How can Mr. Fantastic stretch so far?

Well, let's start off by analyzing some important information about our experiment. The first thing we should discuss is Hooke's Law. When applied to a rubber band, Hooke's Law tells us that:

F = k(x2-x1)

In the case of a rubber band, the k value equals the elasticity constant, while our x2 and x1 equals our starting and end point when stretching each rubber band. Solving this equation will let us know the maximum force that was applied before the rubber band broke. This maximum force will then let us know the tension in the rubber band before snapping. This tension could then be assumed to be the maximum tension that these rubber bands can withstand. When this is applied to Mr. Fantastic, one can understand that, from an observational standpoint, his suit would only allow him to stretch a set maximum distance before reaching it's breaking point. 

So, what would that breaking point be? Well, to find that out we'd have to go into finding his value k. Maybe we could start with the following image...

Yeah, that would take a long while... Well, at least it's something to think about.

Conclusion -

In conclusion, as with all experiments, the element of uncertainty can be found in the data given. With the final stretching data being measure in meters, instead of inches, a fractional margin of error can be added to the data set when converting. For example, 20.5in and 20.6in both show a translation to .52m. While the distance in inches is not the same, the distance in meters is because of rounding. This shows an example of human error and gives the data an uncertainty of at least .1in.

Another interesting topic to bring up is the idea of rubber stretching and shrinking in regards to the temperature it's placed in. Since Mr. Fantastic is called the man of rubber, would he have trouble stretching very far if he was fighting against Ice Man? Would he stretch further if fighting Pyro? 

According to the laws of thermodynamics, heat expands and cold contracts. Rubber (and consequently rubber bands) has the odd property of reversing this idea. Rubber bands actually do the opposite due to their molecular structure. So, if Mr. Fantastic was made of rubber, like his suit, he would actually stretch more against Ice Man and become brittle and shrink when up against Pyro or any other fire based comic book villain. Perhaps this is why he's so mean to The Human Torch.

Lab #1 - Remastered Lab Report.

Rodney Garland

PLAB 223 – 01

11/6/11

Lab #5 – Projectile Motion

Introduction -

This lab entertained the idea of projectile motion and how, at different maximum heights and velocities, an object can fly shorter or farther distances. The point of the lab was to find the initial velocity of the projectile launched, as well as the final distance it reached. Topics and ideas that were key to this experiment include: normal force, the momentum priciple, and the idea of uncertainty.

Procedure -

The first step was to set up the launcher at an angle of 0 degrees. A ball of mass m was then loaded into the cannon and pushed back until one click was heard. The reason behind stopping at one click, is that two or more clicks may add too much power to the shot, sending the ball on a dangerous path of destruction. After prepping the launcher, two meter sticks were obtained and laid flat on the ground, end to end. The meter sticks were then kept in place by use of duct tape. Once the meter sticks were locked into place, two sheets of paper were placed on the ground in places where the ball was thought to land after launch. Finally, the pieces of paper were overlayed by pieces of carbon paper to allow the shots to be measured after impact. The second part of the experiment was just a repeat of the first, except the launcher was set at an angle of 30 degrees.

Data Collection -

Constants –

Initial Height – 1.03m +/- .002m

Mass of Ball – m

Gravity – 9.81 m/s^2

Experiment #1 (Angle at 0 degrees)

Experiment #2 (Angle at 30 degrees)

            Shot #               Distance                 Shot #                     Distance

1	183cm(1.83m)	1	258cm(2.58m)
2	188cm(1.88m)	2	267.5cm(2.675m)
3	184cm(1.84m)	3	260.5cm(2.605m)
4	190.6cm(1.906m)	4	261cm(2.61m)
5	198cm(1.98m)	5	251cm(2.51m)
6	186cm(1.86m)	6	253cm(2.53m)
7	188.3cm(1.883m)	7	261cm(2.61m)
8	192.7cm(1.927m)	8	266cm(2.66m)
9	188cm(1.88m)	9	264cm(2.64m)
10	197cm(1.97m)	10	254cm(2.54m)
Average Distance:	189.56cm	Average Distance:	259.6cm

                               Variance: 15cm                                     Variance: 16.5cm

Data Modeling -

Before this section begins, the following VPython Program can help demonstrate the above data in action and help explain the experiment better:

http://www.megaupload.com/?d=C8CLXSYH

As previously stated, the point of the lab was to find the initial velocity of the projectile after launch. Once the data was collected, the momentum principle can be used to solve for the initial velocity.

The question to ask is, "What do we know?" Well, we know our kinematic equations.

xf = xi + vx(deltaT) (Assuming time at 0)

yf = yi + vyi(t) – 1/2g(t)^2

vfy^2 = viy^2 – 2a(Delta y)

vfx^2 = vix^2 – 2a(Delta x)

In this example, we have these variables on hand.

yi = 1.03cm (The initial height of the launch)

yf = 0 (The ground)

g = -9.81 m/s^2

To find the initial velocity for the horizontal direction, one would simply have to measure the final velocity after launch. Once that number is obtained, they would have to plug it into the formulas and then they will have found the initial velocity.

An example of this is as follows,

ax = 0m/s^2

ay = -9.81m/s^2

xi = 0m

xf = ? (This is what we're looking for.)

yi = The height of the launcher

yf = 0m (Th ground)

xf = xi + vx(deltaT)

yf = yi + vyi(t) – 1/2g(t)^2

Now, we plug in our above values and solve for t(time),

0 = yi + vyi(t) – 1/2(-9.81m/s^2)(t)^2

Once this equation is set up properly, we can use the quadratic equation to finish solving for t. Then, we use the positive value as opposed to the negative and plug that value into the first formula, as the value for deltaT. Once that's done, we can find the final distance the projectile will travel once fired.

This approach will work when dealing with both experiment #1 and experiment #2. The only difference is the change in the angle the ball was launched. This change in angle affects the velocity in such a way that,

vxi = vx(cos(Angle))

And, vyi = vy(sin(Angle))

Knowing the above fomulas can also help you find at which angle the shot was made. If you were to find the initial velocity of the launch, the height of the launcher, and the final distance, you could then use the above formulas to solve this problem.

Conclusion

In conclusion, an experiment like this raises many questions. A few of those questions I will attempt to answer are, "Does the mass of the ball affect the distance the ball will travel?" and "How does uncertaintly come into play when dealing with this experiment?"

To answer the first question, I would like to start by bringing up the idea of air resistance. Although, if you apply the work energy principle to solve for your initial velocity, you'll see that m, which in this case represents the mass of the ball, is part of the equation. However, if you look even further into this question, one could certainly entertain the idea of air resistance to further explain the situation.

To begin, the formula for air resistance is,

F(air) = 1/2pAcv^2

Where,

F(air) = mass of the object x acceleration

p = The density of the fluid (air)

A = The area of the object

c = The drag co-efficient

v = The magnitude of the velocity

Thanks to this formula, it can be shown that a change in the mass of an object will effect the final distance the projectile will reach, thanks to air resistance. However, if the mass isn't that different, for instance, a difference of .00005, the effect of said mass would be inconsequential to the final measurement of the projectile's distance.

The second question can be answered very quickly and simply. In this experiment, uncertainty can be represented in both human error and rounding decimal places. The human error could be found by the ways the measurements were taken. Either a misread of a measurement tool or misuse of a mathmatical formula can be attributed to human error. In this case, the variables that contain uncertainty due to human error include: the initial height and the variance on the final distance calculations. As for decimal places causing uncertainty, a bunch of rounded numbers could cause a loss of precision, if the numbers were rounded prematurely. A quick example will show that,

20.567 + 40.678 = 61.425

And, 21 + 41 = 62

As the list of numbers grow, the final product could wind up a lot different than if a few more decimal places were carried into the equation. A loss of precision like that, could cause rocket ships to explode, which would be a very bad thing.

Another way to solve a possible loss of precision in calculations can be the use of computers. Computers can be used to eliminate human error among other things. Using the Monte Carlo method given in class, you could look at a distribution of data related to finding things such as initial velocity in an experiment like this. In this distribution of data, you could see the measure of uncertainty from 10 shots to 100 shots. Using a computer to find mathematical solutions can help speed up the process of gathering data over time. This method of problem solving will save a good deal of time when discovering the measure of uncertainty as well as general calculations.