Monday, April 20, 2015
Lab #13 Impulse Momentum
Purpose: During this experiment we will be trying to prove that momentum is conserved no matter if it is an elastic or inelastic collision.
Lab #12 Magnetic Potential Energy
Purpose: Since there is no definite formula for magnetic potential energy like kinetic and elastic have, we will be deriving a formula through an experiment that has us recording the force of a magnetic at different scenarios.
This experiment is based on an air track. There is a glider on the track that has a magnet attached to it. Then there is another magnet attached to the track. The other magnet is repulsed by the one on the glider that way they will always be at a certain distance.
For the first part of the lab we had to raise one end of the track in order to measure how close the glider will get to the magnet at certain angles. We continued to raise the track until the distance no longer moves any closer. In the end we measured 6 different times.
The diagram above shows everything that is being measured. However, instead of measuring the height we recorded the angle of the rise.
Below are the six recorded angles and measurements being used. After these were recorded we plugged them into logger pro and used a power fit. We had to change the angles into radians and find the force (mgsin(theta)) of each of the 6 measurements.
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In the end we had to scratch out the last point of our data because when put in with the best fit line the point was pretty far from the curve and the rest of the data.
With the A and B we were able to derive a formula for the magnetic potential energy.
After the formula was derived we are able to continue on to the second part of the experiment. This part was generally the same as the beginning but it instead of angling the track up it is going to be left parallel to the table top. Then we push it gently so that it collides with other magnet and wait for it to stop. During this whole process a motion detector that is connected to logger pro is running and recording the movement of the glider. The motion that the detector is recording is the separation in the calculated columns below.
Once collected we had to create separate calculated columns for separation, kinetic energy, magnetic potential energy (use formula derived) and total energy.
Then we would graph kinetic energy, magnetic potential energy and total energy vs time in order to see that the energies are conserved.
Having the graph stretched out and expanded like it is it is hard to imagine that it is conserved. Generally when a graph is conserved it is a straight line but if we were to expand the graph more it is easier to see.
The diagram above shows everything that is being measured. However, instead of measuring the height we recorded the angle of the rise.
In the end we had to scratch out the last point of our data because when put in with the best fit line the point was pretty far from the curve and the rest of the data.
With the A and B we were able to derive a formula for the magnetic potential energy.
After the formula was derived we are able to continue on to the second part of the experiment. This part was generally the same as the beginning but it instead of angling the track up it is going to be left parallel to the table top. Then we push it gently so that it collides with other magnet and wait for it to stop. During this whole process a motion detector that is connected to logger pro is running and recording the movement of the glider. The motion that the detector is recording is the separation in the calculated columns below.
Once collected we had to create separate calculated columns for separation, kinetic energy, magnetic potential energy (use formula derived) and total energy.
Lab #11 Conservation of Energy
Purpose: The purpose of this lab is for us to be able to see the energies that are working on the spring as it oscillates vertically on a mass spring system.
However, before we can start the actual experiment set up, we need figure out all of the energies that need to be found along with there derivations. Turns out that we need to find elastic potential energy, gravitational potential energy of the mass, kinetic energy of the mass, gravitational potential energy of the spring, and kinetic energy of the spring.
After that is figured out we were able to start recording actual data through logger pro. First thing we had to figure out was our spring constant.
This was accomplished by using the force sensor and stretching the spring slowly while it is attached. Then we graph the force vs position and use the best fit line to get the slope which is our spring constant. The spring constant is going to be needed in order for us to be able to graph the elastic potential energy.
Once that is finished we will actually run the experiment by letting the spring oscillate with a mass hanging at the bottom of it. This data will be used to make the several other calculated columns for elastic potential energy, gravitational potential energy of the mass, kinetic energy of the mass, gravitational potential energy of the spring, and kinetic energy of the spring. We use the formulas derived to put in each individual column.
Our end goal is to have a total energy graph. By graphing all of them in we were able to see if the energy of the spring is conserved. We can see this in the total energy graph by noticing that the graph neither loses or gains energy meaning it is conserved.
After that is figured out we were able to start recording actual data through logger pro. First thing we had to figure out was our spring constant.
This was accomplished by using the force sensor and stretching the spring slowly while it is attached. Then we graph the force vs position and use the best fit line to get the slope which is our spring constant. The spring constant is going to be needed in order for us to be able to graph the elastic potential energy.
Once that is finished we will actually run the experiment by letting the spring oscillate with a mass hanging at the bottom of it. This data will be used to make the several other calculated columns for elastic potential energy, gravitational potential energy of the mass, kinetic energy of the mass, gravitational potential energy of the spring, and kinetic energy of the spring. We use the formulas derived to put in each individual column.
Our end goal is to have a total energy graph. By graphing all of them in we were able to see if the energy of the spring is conserved. We can see this in the total energy graph by noticing that the graph neither loses or gains energy meaning it is conserved.
Lab #10 Work Kinetic Energy Theorem
Purpose: There were two different experiments in this lab. The first is meant to measure the work done on a certain system while the second is meant to measure the kinetic energy of the same system.
Expt 1: Work Done by a Nonconstant Spring Force
We accomplish this by setting a cart on a track then attaching a spring to the end. Then the other free end of the spring is attached to a force sensor. As you can see we have a weight under the spring. That is just meant to have it straighter and more at rest.
Then once that side is set up, on the other side there is a motion sensor that is connected to logger pro.
After the set up is complete we stretched the spring slowly in order to see the work done. The motion detector is meant to monitor the distance the spring is stretched to.
With the data collected we generate a force vs position graph. With this graph we use the best fit line to find the spring constant. Then we integrate it by finding the area under the graph. The integration is the all the work done on the spring.
Our spring constant being 5.724N/m and the work being done is 0.5007 Nm.
Expt 2:Kinetic Energy and the Work-Kinetic Energy Principle
The second part is the same set up as experiment 1. The difference with this one is that instead of stretching the spring slowly we will have the spring already stretched and have the cart spring back along with the rest of the system.
With this experiment we will be able to find out the work done by the spring itself. Then after that is done we graph it the same as before then integrate in order to find the work. However, for this graph we are going to add in kinetic energy just as an extra comparison. In order to get kinetic energy we had to add an extra calculated column then include it on the graph.
We have three graphs at different positions in order for us to see that the work is consistent throughout the whole system. Since kinetic energy and force are very different we had a major source of error somewhere in our experiment.
Expt 1: Work Done by a Nonconstant Spring Force
We accomplish this by setting a cart on a track then attaching a spring to the end. Then the other free end of the spring is attached to a force sensor. As you can see we have a weight under the spring. That is just meant to have it straighter and more at rest.Then once that side is set up, on the other side there is a motion sensor that is connected to logger pro.After the set up is complete we stretched the spring slowly in order to see the work done. The motion detector is meant to monitor the distance the spring is stretched to.
With the data collected we generate a force vs position graph. With this graph we use the best fit line to find the spring constant. Then we integrate it by finding the area under the graph. The integration is the all the work done on the spring.
Expt 2:Kinetic Energy and the Work-Kinetic Energy Principle
The second part is the same set up as experiment 1. The difference with this one is that instead of stretching the spring slowly we will have the spring already stretched and have the cart spring back along with the rest of the system.
We have three graphs at different positions in order for us to see that the work is consistent throughout the whole system. Since kinetic energy and force are very different we had a major source of error somewhere in our experiment.
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.
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.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.
With this information on the table we had to plot the acceleration vs angular speed^2.
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.
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.
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.
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.
Sunday, April 12, 2015
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.
The way we accomplish this is by finding the density of three metallic cylinders and then calculate the density of an unknown object.
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.
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