Lab #9 Centripetal Force Motor

Purpose: We are meant to find the relationship between theta and omega of the apparatus.

 We accomplish this by recording the time the rubber stopper makes a rotation and measure the height of the stopper from the ground (h).

However, before we can start any of that we would have to record the radius, length of the string (L) and height of the apparatus (H).
L= 1.645m
R=.98m
H=2m

Once all measurements are gathered we had to come up with our formulas for theta and time before we started recording times and finding h. Theta was found by using a right triangle with the hypotenuse as L and the height as H-h. Then we figured out time by drawing a force diagram of the rubber stopper and solving for omega and replacing to solve for time.

After the formulas were derived we had to start our actual experiment. The object of this part was to record the time of ten rotations. Then have a ring stand with a horizontal piece of paper tap the bottom of the stopper in order to get h. We did this 6 times at different speeds in order to get different angles.


After all is recorded we plugged everything into our previously derived formulas to get the theta and time of each test. However, to make sense of everything gathered and collected we charted all of the calculated thetas and times.

This graph represents the actual and theoretical times we figured out. By figuring out the best fit line of the graph we can see how accurate our data was.

Lab #8 Centripetal Acceleration vs. Angular Frequency

Purpose: This demonstration was meant for us to be able to determine the relationship between centripetal acceleration and angular speed. We accomplish this by attaching an accelerometer to a spinning wheel. Then have a photogate attached to a pole setup up so it can record the period of the rotating wheel.

The rotation was recorded 6 times at 6 different speeds. We gathered our acceleration by by taking the average of the recorded acceleration vs time graph.

Once that was recorded we needed to calculate the velocity in order to plot the acceleration vs angular speed graph. The way we calculated omega (angular speed) is by deriving the formula from v=w/r and a=rw^2. Then everything is recorded in a table on logger pro.

With this information on the table we had to plot the acceleration vs angular speed^2.

 As you can see the graph is pretty linear meaning the experiment was pretty consistent throughout the every step. Especially since the correlation says 0.9999.

Lab #7 Trajectories

Purpose: Use projectile motion to predict where the ball will impact an inclined board.


With this set up we have to launch a ball from some point on the ramp then let it hit the floor where the carbon paper is. We launch the ball several times in order to make sure that the point of impact is generally the same.











The carbon paper was able to mark where the ball landed each time. Ours turned out to be around 0.701m from the table with the angle at around 25 degrees.


Once that is gathered we calculated the speed and time of the ball launch using the measurements recorded.

It turns out the velocity is 1.59 m/s while the time is 0.44 second.

For the second part of the experiment we had to predict where the ball would land if it were to blocked by a slanted board. We accomplished this by using the velocity and time gathered in the first part.

We predicted the distance to be 0.487m along the incline. After the derivation we are able to run the experiment to determine the actual distance the ball hits on the board.


This is the setup with the inclined board and the carbon paper attached. We do the same thing as we did in the first part. Launch the ball a couple of times in order to get a general location then find the average.











The actual turned out to be around .488m along the board which was pretty close the one we calculated before hand. However, we could not just end it here. We need to calculate the uncertainty because the tools being used all have a certain amount of accuracy. So after the calculation we gathered the distance to be 0.488+/- .0315. All the work is shown in the photo below.

Our experiment was pretty successful because the distance we came up with was generally the same as the one calculated.

Lab #6 Modeling Friction Forces

Purpose: There are multiples of different ways to model friction. In this lab we will be covering five procedures along with all of the derivations and appropriate graphs that come along with it.

Experiment 1: Static Friction
In this experiment we will attach a cup of water to one end of a string and the other to a block of wood. The side of a string with the cup of water will dangle off the table going over a relatively frictionless spring, while the block is on a track.

Lab #5: Propgated uncertainty in measurements

Purpose: The reason for doing this lab is to have the students practice how to calculate the uncertainty of our measurements when collecting data with the measuring equipment.

The way we accomplish this is by finding the density of three metallic cylinders and then calculate the density of an unknown object.

(In the photo we accidentally put the wrong metal on the wrong name)

Then in order to find the density we used filled in the formula d= (4 m) / (π h d^2).

These were the density. Then we calculated the uncertainty to go with them.

 

We found out in the end we mixed up our rod measurements making the iron not actually 
iron it was lead.

As for the second part of the lab, we had to determine the mass of an unknown weight hanging 
at an angle.

 

First we measure the angle.

Then we looked at the force that it took to hold the weight up. Then we calculated the mass with

measurements.

Once done we used all the measurements along with there uncertainties to calculate the entire

and uncertainty.

Through this were able to calculate the uncertainties of all the tools.

Lab #4: Air resistance

Purpose: This lab is designed to have students figure out the relationship between air resistance force and speed. The way that air resistance works on a object depends on the objects shape, speed and the material. We use the formula F_resistance = kv^n. (k represents the objects shape and area)

We accomplish this by dropping coffee filters and dropping them from a certain height. By recording the drop with a video camera and putting the videos into Logger Pro we were able to dot the drop of the filter and get its velocity.

 The dots about to be seen represent the distance the filter went for each frame of the recording.

 

We were able to determine the velocity of the coffee filter drop by finding the slope of a distance vs time graph.

So the velocity for one coffee filter falling is 0.7959m/s. We repeat this process with two, three, four and five coffee filters in order to use them to get our k and n value through graphing the velocities along with the forces.

 So with our graph we determined that our k=0.01249 and n=2.022.

Once that was determined we were able to model the fall for each in Excel.

By changing the mass we would be able to determine the ending velocity. As long as you stretched the columns until acceleration became zero.

coffee filter #1

coffee filter #2

coffee filter #3

coffee filter #4

coffee filter #5

We ended with all our velocities with an acceleration of zero.

Lab #3: Non-Constant accelertaion problem

Purpose: This lab is meant for people to see that sometimes solving a problem using calculations and calculus is not the way to go. Because things can get complicated really fast.

For example this problem:

If a person were asked to solve for how far the elephant would go before coming to rest, it would a nightmare. The calculus to solve this problem is not impossible but difficult and time consuming.

However, there is another way to find the distance and time the elephant goes. That would be by using Excel and solving with numerical integration. By choosing an interval like 0.1 to set the time at and calculating the acceleration, average acceleration, change of velocity, velocity, average velocity, change in position and distance we will be able to find the time and position if we extend the graph far enough.

By extending the graph all the way down until the velocity almost reaches zero we can see the approximate time and distance found the elephant has traveled.

We were able to test other time intervals to see how close the approximation can get or how far estimate will be.
                                         0.05 sec:

                                        0.2 sec:

                                        1 sec:

As you can see all of the graphs had relatively the same time and distance gathered. Some being closer to the calculated actual then others.