Oct-9-2014 The Mystery of the Magnet

Purpose:
Magnets with same ends behave like springs. They push away from each other. But unlike honest springs, magnets are troublesome and mysterious. They don't behave according to a convenient rule like hooke's law . In comes the students, whose job this time is to find a relationship between the force a magnet exerts and the distance between the magnets.

Lab:
The students will solve the mystery by setting up a system where they can measure the force vs distance of colliding magnets and see if the energy is conserved after collision.
This is done with an air track to create a frictionless surface and a glider with a magnet attached. And a motion sensor.

The air track was put on a slope so that the glider would accelerate toward the magnet. The angle of the slope was recorded.

The angle was changed five times and the experiment repeated. Students used this data to plot force vs distance.

Students used the force vs distance graph to find the relationship of energy of the magnet.

The students then repeated the experiment on a flat angel and a motion sensor to find velocity and position vs time. They used this information to create a graph of the potential and kinetic energies. 

Conclusion

The red in the graph is the total energy and the graph shows that energy was mostly conserved barring air friction.

Oct-7-2014 Is energy conserved?

Purpose:
Students will show that energy is indeed conserved throughout the universe. Or find that it's not and probably win a nobel prize. Students will do this by setting up a system where energy fluctuates between potential and kinetic energy and see if energy is conserved throughout.

The Lab:
Students will attach a mass to a spring that hangs vertically. The mass will then be pulled down by gravity while the elasticity of the spring will pull the mass back up. The energy of the system will then be fluctuating between the gravitational potential energy of the mass/spring, the kinetic energy of the mass/spring, and the elastic energy of the spring.
The students will record of all these changes with a motion sensor and some clever physics calculations. They will add up all the energies to see if the total energy stays constant which theoretically it should barring alien interference.

Here is a picture of the student's heartfelt effort:

Here are the student's calculations:

Elastic PE in spring: 1/2 K (stretch)^2

KE of mass : 1/2mv^2

PE of mass:   mg * y

PE of spring: m(spring) / 2 * g * y + mgh/2  *h  = height of top of spring and y = bottom of spring

KE of spring 1/2 m(spring)/3 * V^2(mass)

GPE: 1/2 m(spring) * g * y (y = bottom of mass height)

The students then used logger pro to graph all of the energy over time. Then the students added all the energies to find the total energy and graphed that. After some clever menagering of the data with the professor's help the students were able to produce a total energy graph that was almost a straight line:

Hint: it's the light green one at the top

Conclusion:

Yay! The experiment was a success! Energy is conserved! All physics is saved!

Oct-2-2014 Observing the relationship between work and energy

Purpose:
Students conducted a lab to observe the relationship between work and energy.

Lab:
We set up a track with a rolling cart with a spring attached. There is a motion sensor on one end and on the other end the spring is attached to a force sensor. We zero both sensors with the spring at rest. Then we turn both sensors on, pull the cart and let go. The varying force and position data is then recorded.

Setup:

Calculations:
The motion and force sensor gave us the data for velocity, force, time and position. Students calculated kinetic energy using the mass and velocity (.5mv^2). Students then plotted a graph of kinetic energy vs position, and force vs position. The students then took the integral of a section of the force vs position graph and compared it to the kinetic energy for the same section. Theoretically the data should be equal. The students found their data to be within reasonable bounds for error.

Sept-25-2014 Test of Strength

Purpose:

Students had to do manual labor in order to have an intuitive understanding of work and energy.

Lab Part 1:

Students would hang weights from a balcony with a pulley system and calculate the time it takes them to pull the weights to the top of the balcony.

Balcony Pulley System:

First the students had to measure the height of the balcony.
There were stairs leading to the balcony so the students measured the height a single stair step and counted the number of steps.
They used that to calculate the height of the balcony.
The students then picked one of three masses, from 5 to 9 kg. And were timed on how fast they could pull the weight up to the height.

The height of the balcony was 4.29 meters. The mass of the object x gravity x the height of the balcony would equal the energy needed to move the object to the top of the balcony.

This divided by the time it took to move the object would provide the students power output.

The student calculated his energy and power output as such:

Energy
(5kg)(9.8m/s^2)(4.29m) = 210.21 joules

Power
210.21 joules / 10.49 seconds = 20.04 watts


Lab part 2

The students would record the energy and power it would take them to walk up and down the stairs at a constant speed. The students recorded the time it took for them to walk up and down the stairs. The students then used the same method as in part 1 to calculate Energy and Power.

Energy
(50kg)(9.8m/s^2)(4.29m) = 2102.1 joules

Power
2102.1 joules/ 14.5 seconds = 145 watts              (walking up)
2102.1 joules/ 7.25 seconds =  290 watts             (walking down)

Sept-23-2014 A spinning mass and its relationship to an angle

Purpose:
In this lab students will devise a relationship between angular velocity and an angle created, use that to calculate angular velocity and compare that with the actual angular velocity.

Lab:

The Professor sets up a motor powered contraption that spins a stick around with a string and a mass tied to the end of the stick. As the stick spins faster the mass gains velocity and spins at a taller height, while the angle between the string and the stick decreases.

Setup:

Students will start by measure the height of the stick off the ground, the length of the stick, and the length of the string.

The Professor will then set the motor to spin at a certain constant velocity and the mass on the string will rotate at a set height. Students will then measure the height the mass reaches. And also record the time the mass takes to complete 5 rotations.

Measuring the height of spinning mass:

This process was repeated a total of seven times with each repetition at a higher velocity and height.

After the data was recorded, the students then drew a model of the apparatus to find a relationship between the speed of the stick and the angle created between the string and the stick.

Model: 

The students then used this model to come up with a relationship between the angular velocity of the stick and the angle between the string and the vertical line from the tip of the stick to the ground.

The formula the students came up with was 

The students then set out to confirm their formula by comparing it to the formula w = 2pi/T.

The students used excel to find the numerical values needed.

Excel plot:

They then plotted a graph of the w found from the students equation and w found from w=2pi/T.

The students expected the graph to have a 1 to 1 relationship and therefore the slope to be 1, but that was not the case. Clearly something was wrong with the data or calculations.

The students conjecture the calculations may have been off for the formula relating w to theta. Or the data collection of the period may have been incorrect.

Sept-23-2014 Finding the relationship between alpha and omega on a spinning disk

Purpose:

The professor spins a disk with a measuring device attached to it that will measure the angular acceleration. The students will use this to calculate the angular velocity.

Lab:

The Professor sets up the lab by taping a measuring device to a disk that can spin. He then spins the disk at some speed with the device on. The device will measure the angular acceleration. The students then record the time it takes for the disk to complete 5 revolutions. This will provide the students with the period.

Spinning Disk:

The Professor then spins the disk at some speed with the device on. The device will measure the angular acceleration. The students then record the time it takes for the disk to complete 5 revolutions. This will provide the students with the period. The Professor spins the disk 5 times with different force. The students record the data each time.

Data:

The students then use the period to calculate angular velocity with the formula w=2pi/T.
Theoritically angular acceleration and angular velocity should have a linear relationship. The students tested this by graphing angular acceleration vs angular velocity.

Graph:

Conclusion:

As seen in the graph, the students found through the experiment that angular acceleration and angular velocity were shown to have a linear relationship in this case.

Sept-18-2014 Determining coefficients of static and kinetic friction on a sloped surface

Purpose:

Students will determine the static and kinetic friction coefficient of a block on a sloped surface.

Lab:

The students used a metal track to provide a sloped surface.

Setup:

The students then placed a wooden block on the ramp and adjusted the height of track to the point where the block just starts to move. This would allow the students to calculate the static friction coefficient.

The students then measured the height and length of the track and using the pythagorean theorem found the angle of the track.

With this information the students followed the problem solving steps in physics and created a Free Body Diagram and determined the forces acting on the block. Through these calculations, the students found the static friction coefficient.

Calculations:

The students calculated the static friction coefficient to be 0.3.

The students used the same setup to find the kinetic friction coefficient.
The students raised the ramp this time allowing the block to slide freely over it. Then the students used a motion sensor to record the blocks velocity vs time. The students determined the slope of the graph would be the acceleration.

Graph:

The students also measured the height and length of the ramp to find the angle of the ramp.
With this data the students then drew a new Free body diagram and used it to calculate the kinetic friction coefficient.

Calculations:

The students found the coefficient of kinetic friction to be 0.386.


Conclusion:

The students were able to utilize their knowledge of physics to determine the coefficient of static and kinetic friction with experimental data. Lab success.

Sept-18-2014 Determining kinetic friction coefficient

Kinetic Friction

Purpose:

Students conducted an experiment to determine the kinetic friction coefficient between a block and a table.

 Lab:

The lab was accomplished using string, block(s), and a force sensor. It was setup in this way:

The block was connected to the force sensor through the string which would allow the students to record the force necessary to pull the block.

The students first had to zero the block through logger pro to minimize error in data collection. The students then measured the mass of the block and recorded it and then pulled the force sensor at a constant velocity to record the force necessary to move the block.

The force was displayed through a graph: 

The slope of the velocity vs time graph was determined to be the average kinetic friction force.

The experiment was repeated five times with a block added each time. The mass of the blocks and the average force from the force sensor was recorded each time into a table:

The students then used the data to plot a graph of Normal force vs Kinetic friction force and as explained in the static friction lab, the slope of this graph would theoretically be the kinetic friction coefficient.

Graph:

Conclusion:

The students were able to determine a kinetic friction coefficient through hands on lab experience. The kinetic friction coefficient was determined to be 0.2887 from the lab.

Sept-18-2014 Determining Static Friction

Purpose:

Students will use an experiment to determine the static friction coefficient of an object.

Lab:

The students assembled a lab setup that would allow them to measure the static friction coefficient of an object with a table. The accomplished this with a pulley, string, a cup, and a wooden block with felt on one side.

The mass that will be used to determine the static friction coefficient is the wooden block so the mass of the block was measured so that the students would be able to calculate the normal force that the table would have on the block.

Then the components are assembled as shown:

The block is placed on the table with the felt side down and a string is tied to it. the string is then looped on a frictionless*, massless* pulley and the other end is tied to a cup. 

Once the setup is complete the students then took the following steps. They added water to the cup until just the point when the block would start moving. They then measured the mass of the cup and water. The students repeated these steps five times. Each time with an added block to increase the mass and therefore the Normal and ultimately the frictional force the block would have with the table.

The Mass of the block(s), the mass of the water+cup, and the Normal force between the table and the block was recorded and kept track of in a table:

The students then determined that the max static friction force was equal* to gravity x the mass of the water&cup. Also, friction force equals the coefficient of friction x N. 

Therefore in order to find the static friction coefficient, students plotted the graph of Normal force versus the max static friction force. Since slope is y/x, in this case it would be Normal force/ max friction force which would theoretically yield the max static friction coefficient.

The Graph:

The graph displayed a slope of .3865 which the students took to be the max static friction coefficient.

Sept-16-2014 Calculating mass of object

Purpose:
Students calculated the mass of an object by measuring the force needed to hold the object in place.

Lab:

The lab came pre-set up as shown:

A string which held up an object is tied to two force measures that record the force needed to hold up the object.

The students first had to reset the force measures to zero to try to reduce error as much as possible. The students then attached the object to the string and let gravity pull the object down and the strings hold them up.

The students then recorded two key pieces of data from the experiment: the force being recorded on the force measures and the angle of the two parts of the string.

With these two pieces of data students then calculated the mass of the object.

Mass calculation:

Students then accounted for the error in the data with a data analysis by taking into account the a possible angle error of 2 degrees because of the angle measure and human error and the possible error of 0.5 newtons because of the inaccuracy of the force measures.

Error Analysis:

Conclusion:

Students successfully calculated the mass of an object with the use of force measures and string.

Sept-16-2014 Calculating Density and Error Analysis on Aluminum, Copper and Steel

Purpose:

This lab will teach students to perform error analysis on data gathered from experiments.

Lab:

Students were given three cylinders of different materials: Aluminum, Steel and Copper.

Students then used a caliper and mass scale to record the height, diameter and mass of the three cylinders.

A simple volume calculation was done to find volume and with the mass and the volume the students calculated the density of the cylinders with the equation d = m/v.  All of the data was written onto a whiteboard.

Then an error analysis was performed by taking into account the error of the mass scale which had an error of .01 grams and the caliper which had an error of .01 cm

The calculated density for the three materials aluminum, copper and steel along with their respected calculated errors were then compared with the textbook densities for the materials and it was found that the textbook densities were within the student's calculated error range.

Conclusion:

The students successfully calculated the density of the three materials with an error range that met the established 'actual' densities of the three materials.