14-Oct-2014: Collision in Two Dimensions

Purpose:
The purpose of this lab is for students to observe two-dimensional collision and determine if momentum and energy are conserved.
Apparatus:
The camera, attached to a pole, looks down at the glass board, and is able to view the entire board. By placing two balls on the board, the camera should be able to record the motion of both balls along a
xy-plane. The camera should be set up properly: shutter should be zero, reduce exposure, and increase gain so that camera can see the motion of both balls clearly. One ball should be set in place, while the other ball comes into contact with it at an angle, so that both balls should move at different angles.

Explanation:
With the apparatus all set up, we recorded to different trials: steel on steel and marble on steel. The first trial was steel on steel. One steel ball was set in place, and the second one was aimed to hit the stationary ball at an angle. With the camera recording, we rolled the ball out and both balls moved at different angles away from each other and at different speeds. We used the recording and traced the paths of both steel balls, and came up with position and velocity in x-direction and y-direction for both steel balls. We set the coordinates so that the origin is where the rolling ball first moved. The x-axis is aligned with the motion of the rolling ball so that the y-direction had no value until the balls collided.

By finding the slope of each line before the collision and after the collision, we are able to find the average velocity of each line. With the velocity, can find kinetic energy in the x and y-direction. The energies need to be consistent throughout the procedure of this lab. By plotting the energies on one graph we can see that the kinetic and potential energy has a slope closely to zero, which means that energy was not lost through the procedure.

Also, with the velocity, we were able to calculate the momentum of this trial. The initial momentum for both x and y-direction were both slightly larger than the final momentum, by a percent difference of 0.409%. During the collision, the rolling ball was spinning vertically, which is believed to have lost some energy in the spin.

The second trial was marble on steel, where the marble is the stationary ball, and the steel ball is the rolling ball. Since the steel ball is heavier than the marble ball, the motion of the marble after the collision will be more faster in general in comparison with the first trial. Knowing that the marble ball has a faster velocity, we can still assume that the energies are conserved in this procedure. We graphed the position of x and y-direction vs time, just like in trial 1, and found the velocity of each different motion.

 With the velocity, we can find the kinetic energy  for both balls. From the graph, we see that the energy has a slope of zero, which means that the energy was conserved.

After calculating the momentum, we can conclude that momentum was conserved with a percent difference of 13.8%, which is quite large since the value is higher than 10%. This is due to the difference in the mass, and the spin in the steel marble after the collision; the spinning was a cause of energy lost.

Conclusion:
In this lab, we discovered that energy and momentum was conserve by graphing kinetic energy and calculating the momentum of the initial velocity to the final velocity. There were lost in energy and momentum when the steel balls was spinning after the collision.

9-Oct-2014: Impulse

Purpose:
The purpose of this lab if for students to observe impulse through elastic and inelastic collision.
Apparatus:
There are two parts to this lab experiment. The first part is to find impulse through elastic collision, and to do that, we need the help of spring collision. We place the track on a level surface, with a cart at one end and a motion detector at the other end. The cart held in place at one end of the track has a spring connected to the cart, and is released in order for the collision to happen. Then, we place a force sensor on another cart, that is placed anywhere on the track. The second part is where we add mass to the cart in motion. The impulse should be larger since there is more mass. The third part is where we take the spring cart away and replace it with a wooden stock that has clay pasted on the wooden stock. Also, the force sensor needs a nail in place of the rubber stopper. With these equipments, we should produce an inelastic collision.

Explanation:

For Part 1 of this lab, we first calibrated the force sensor to read zero, and set Logger Pro to record force and distance. Giving the cart, on the track with a mass of 440g, a light push, the cart ran across the track and into the spring. With the proper data collected, we graphed force vs time and velocity vs time. Using the force vs time graph, we integrated the curve created by the change in force throughout a period of time, and came out with an impulse of 0.3136 N*s. Using the velocity vs time graph, we searched for the initial velocity, right before the collision, and the final velocity, right after the collision, and used the impulse equation to find the momentum of this system, which came out to be 0.292 N*s. The percent error was 6.89%, which is acceptable. The error was due to which instantaneous velocity we picked on Logger Pro. If we were to pick two different velocity, we may be able to decrease the percent error, but Logger Pro can only count to a certain decimal point. Also, the collision was not perfectly elastic, so there could have been some energy lost during the collision.

For Part 2 of this lab, we added mass to the cart, and the total mass came out to be 940g. With the same procedures as Part 1, the force vs time graph gave us a impulse of 0.7786N*s. Using the velocity vs time graph, we came up with an momentum of 0.8366N*s. The percent error was 7.45%, which is acceptable. The cause of the error was the same as Part 1, but only more heavily, due to the increase in mass. With the extra 500g, there were more energy lost during the collision.

For Part 3 of this lab, we replaced the cart with spring with the wooden stock and clay and the rubber stopper with a nail. Same as Part 1, we pushed the cart lightly, and the cart ran across the track and into the clay, stopping the cart completely. Graphing the force vs time , we can integrate it to find the impulse, which came out to be 0.1869N*s. Graphing the velocity vs time, we were able to find the initial velocity and final velocity. The mass of the cart was 0.44kg, so we calculated the momentum of the system to be 0.1892N*s. The percent error was 1.23%, which is almost zero, and considerable acceptable. This trial had less error because the purpose was to exert all the energy out of the cart and into the clay, so the only error came from Logger Pro.

Conclusion:

In order to find impulse and momentum, we had plot force vs time graph and velocity vs time graph. The impulse was found by integrating the force vs time graph, and the momentum was found by finding the initial velocity and final velocity and using the momentum equation. The impulse and momentum were almost equal to each other, which means that this system follows true with the impulse-momentum theorem. The error we found in this lab was due to Logger Pro's accuracy and the lost in energy in the collision. Other than that, the system was accurate.

7-Oct-2014: Spring Collision

Purpose:
The purpose of this lab is explore the conservation of energy in magnetic forces. Also, to find the equation of forces between two magnets.
Apparatus:
There are two parts to this experiment. The first part is to find an equation for the forces between the magnets. By tilting the track up at the other end of the track, we find the cart moves closer to the track, and with the force coming from the mass of the cart, we can find the force exerted on the magnets, and plot a force vs. position graph to find the equation. The second part of this lab is to determine if the energy throughout the experiment was conserved. To do this, we leveled the track and attached a motion detector at one end of the track. We then pushed a frictionless cart with a magnet at one end of the cart to the end of the track with a magnet attached to that end. With the magnets pushing off each other the cart should move the other direction.
.

Explanation:

For the first part of the lab, we raised the track at several different heights. For each certain heights we can observe the distance between the magnets decreases as the height of the cart increases. We took eleven different measurements, and with the mass of the cart, we can measure the force of the magnets by using the angle between the track and table. With the measurements forces and distances, we graphed a force vs distance chart, and found the equation of the forces, 1.285x10^-7r^-4.893. We had to cross-out four points to obtain a perfect logarithmic curve.

For the second part of this lab, we leveled the track and placed the motion detector at one end of the track. With Logger Pro set up, we pushed the cart, with a magnet in the front of the cart, towards the magnet where the motion detector is. The cart starts with an initial velocity; once the magnets come close to contact, the frictionless cart slows down and eventually, for an instance, hit zero velocity before moving in the opposite direction. Once the magnets exert force off each other, potential energy increases and kinetic energy decreases. To find the kinetic energy, we used the equation 1/2mv², and for potential energy, we integrated the equation we found in part one of this experiment, which gave us -3.3x10^-8r^-3.893. We plot the kinetic energy, potential energy, and the total energy on one graph and the results were as expected. The total energy should show close to a linear line while the kinetic energy and potential energy shifts at the point were the magnets come close together. With these results, we can assume that energy was somewhat conserved. But the point were the magnets almost meet, there was a lost in energy and this was recorded by Logger Pro. We believe that the lost in energy was due to how the cart lifts a little.

Conclusion:

To assure that the system of this apparatus has conserved energy, we first found an equation for the magnetic potential energy. To do this, we raised on end of the track and found the distance between the track; the higher the track was lifted, the smaller the distance was between the magnet. With this equation we were able to confirm that some energy was lost but most of the energy was conserved.

7-Oct-2014: Spring Energy

Purpose:
The purpose of this lab is for students to experience with the spring energy, and to discover how the energy is transferred from potential to kinetic and vise-versa.
Apparatus:
We calibrated the force sensor and set it up on a stand facing down. We hung a spring on the force sensor with weights hanging on the spring. We set the motion detector at the bottom of everything to measure the distance the spring moves. After the set up was complete, we zeroed every measurement on the Logger Pro.

Explanation:

With the apparatus set up, I pulled the mass down, which stretched the spring, until the mass was right above the motion detector. I released the mass once Logger Pro was ready and it recorded the force and distance it traveled. Using the velocity and mass, we found the kinetic energy of the system. Using the mass, gravity and position, we found the potential energy of the system. Using the potential energy we found previously, we set the potential energy equal to the elastic potential energy, giving us k constant to be 16.68. The distance for the potential energy was the distance traveled plus the height of the spring unstretched. On the other hand, the distance for the elastic potential energy was the distance unstretched minus the distance read by Logger Pro. The distance unstretched was found by finding equilibrium height, 0.625m, subtracting the distance distance from the equilibrium to the unstetched, 0.294m. The distance unstretched for the elastic potential energy is 0.331m, and the distance unstreched for the potential energy was the position read by Logger Pro plus 0.75m. Using the mass of the spring, 0.045 kg, and the velocity, we found the kinetic energy of the spring; and with the distance traveled by the mass, we found the potential energy of the spring. When the potential energy of the spring reaches it's max, the kinetic energy of the spring will reach a value of zero. When the potential energy of the spring reaches a value of zero, the kinetic energy should reach it's max. Adding both the potential energy of the spring and the kinetic energy of the spring, we should get a small range of numbers, which we called total energy. When we graph the total energy, the plot was close to a straight line.

The instructions of the lab.

Finding the change of position from equilibrium

All calculations are done on Logger Pro.

Conclusion:

With the spring pulled away from equilibrium position, we found that the energy throughout the spring transfers from kinetic energy to potential energy and back to kinetic energy and so forth. With the mass attached to the end of the spring, we find that the spring had more energy and traveled more further from equilibrium point. Adding all the energy together, we find that the total energy was close to constant, which means that the energy was close to conserved. The reason why the energy was not so conserved was because the gravity pulling the hanging mass and the mass of the spring is another constant energy.

30-Sept-2014: Spring Work

Purpose:
The purpose of this lab is for students to explore the work of spring when stretched from initial position and released at a certain distance from initial position.
Apparatus:
We place a motion sensor at one end of the track and a cart attached one end of the spring. The other end of the spring was attached to a force sensor at the other end of the track. The force sensor is held in place by a c-clamp that was screwed onto the side of the table. The middle of the spring was held up by a block to avoid any additional error. After collecting the data of spring work for the cart alone, we measured the work of the cart with mass on the cart.

Explanation:
We set Logger Pro to read the force from the force sensor and the distance with the motion detector. The cart, with masses on the cart, gave a total mass of 1.405 kg. As we pulled the cart away from the force sensor, the force sensor read about 3.7N of force. As we release the cart from the stretched position, we collected the data of force vs distance. With the mass and velocity known, we were able to calculate the kinetic energy. Using Logger Pro, we found the integral of the force, which gives us the work of the spring, giving us a value of 0.4484m*N. The total kinetic energy, measured by the equation we inputted in Logger Pro, 1/2mv², was 0.394J. The percent error was 12%, which is considered quite large, knowing that the percent error is higher than 10%. There was large error accumulated when collecting data. For example, when the spring was contrasting, the wooden block was also pulled as well, causing friction between the block and the track. Another cause of high percent error was the force sensor was not reading a value of zero after calibrating the sensor.

Conclusion:
In this lab experiment, we measured spring work using a force sensor and motion detector. We needed to find the force of the spring when the spring was stretched a certain distance, and the mass of the cart with masses in the cart. With all this, we were able to find the kinetic energy. Once we have force and kinetic energy, we compared the energy from the equation to the energy calculated from Logger Pro, giving us a percent error higher than 10%. There were too much error around the apparatus that we were not able to get a accurate reading.

16-Sept-2014: Circular Motion

Purpose
The purpose of this lab is for students to experience with rotational motion. Students are to find and calculate certain measurements with given information about the rotating object.
Apparatus
There are two part to this lab: the first is a rotating disk and the second is a motor that rotates a hanging object from a string that is attached onto a stick. The first part was done as a class, several students timed the period of each rotation, and the actual speed was measured by LoggerPro. The second part was done in groups and each group measured the time of each period as the professor monitored the motor and the speed of the rotation. To measure the angle, we used a stand with a piece of paper attached onto a bar. Students were to find the height of the stand, the distance of the stick from center, and the length of the string.

Explanation
The first part was to rotate a solid disk, which was spun by the professor, and the time was recorded by several students. As a class, we resulted with several different times, similar but different, and we averaged the time. With the average of the time, we then found the acceleration for the five trial rotations. Then we graphed an omega vs. acceleration plot chart and found that the correlation was close to the value of 1.

Before starting the second part of the lab, we solved for an equation that shows the relationship between omega and angle; as angle becomes larger, so does the omega. Each group were to find the time it took for a number of revolutions, and the class found the height of the hanging mass was measured from one student in the class. With the height of the hanging object, we were able to find the angle created from the string and hanging object. With the distance of the stick, the length of the string, and the angle, we measured omega with our equation. Comparing the measured omega and the actual omega, we get a correlation of 0.9851, and the percent error were below 4%.

Conclusion
Circular motion deals with omega and period, which are measurable. For period, we measured the time it takes for one revolution. For omega, it took a little more effort to find an equation that gives omega. We calculated an equation of omega depending on the angle, so we concluded from the equation that if the angle grows larger so does the omega.

18-Sept-2014: Modeling Friction Forces

Purpose:
The purpose of this lab is to explore with static and kinetic friction by applying force in a few different ways.
Apparatus:
There are five parts to this lab, and each part is different from each other in terms of which friction we are dealing with and how we use certain materials to find the coefficient of friction.
Part 1: We placed a wooden block with felt, on one side of the face of the block, facing down on the table to give friction between the table and the block. We tied a string to the block and over a pulley at the edge of the table. At the other end of the string is a cup with a paperclip use to hold up the cup. With this setup, we added water into the cup until the block starts to move, which then we can measure the mass of the cup and block. We repeat this step while adding an extra block on top of the original, until the 4th block.

Part 2: We connect the force sensor to logger pro and opened up the file Coefficient of Kinetic Friction.cmbl to set up sensor. Then, calibrated the force sensor using a 500-g hanging mass. Afterwards, we placed the force sensor on the table and Zero the force sensor. We measured the mass of the block. We tied a string to connect the force sensor and wooden block with felt underneath, and started collecting data. The data collect a force from us pulling on the force sensor at a constant force. Repeat this step with one extra block each time, until 3rd block is added.

Part 3: In this part of this lab, we needed to find static friction. We placed the block with the felt side faced down on a ramp, and then we slowly lifted the ramp until the block starts to move. At that angle, we can calculate what the static friction.

Part 4: For this part of the lab, we needed to find kinetic friction. Same as Part 3, we placed the block with the felt side facing down on the ramp, but the ramp is at an angle larger than the angle from Part 3. With Logger Pro, we can record the data of the block accelerating toward a sensor at the bottom of the ramp. With the velocity vs time graph, we can find the acceleration by plotting a fit line.

Part 5: With the same step up as Part 4, we added a pulley at the top end of the ramp, and tied a string to the block and a mass weight to the other end. By dropping to mass weight, we see the block accelerate towards the top of the ramp.With the kinetic friction, we can find the theoretical acceleration, and compare the actual to the theoretical.

Explanation

Part 1: For Part 1 of this lab, we did four different trials, adding an extra block with each trial. With the mass of the blocks and the mass of the cup and water, we came up with the normal force between the block and the track and the static friction between the block and the track. 

Number of blocks on the track	Total mass of blocks on traks (kg)	Mass of water+cup when the blocks just started to move (kg)	Normal force between the block and the track (N)	Maximun static friction force between the block and the track (N)
1	0.1474	0.0607	1.44452	0.411804613
2	0.245	0.0909	2.401	0.371020408
3	0.3929	0.1473	3.85042	0.374904556
4	0.5311	0.1795	5.20478	0.337977782

Part 2: We pulled the force sensors, that was tied to a string on one end and the other end to the block with a felt side faced down, with a constant force that gives us a data plot, from Logger Pro, showing a rigid horizontal line. We did four different trials, starting with one block and adding another block with each trial, giving us four different results. We plotted a graph of Kinetic friction vs. Normal.

Number of blocks on the track	Total mass of blocks on tracks (kg)	Normal force between the block and the track (N)	Average kinetic friction force between the block and the track (N)
1	0.1427	1.39846	0.6043
2	0.2807	2.75086	0.6748
3	0.4287	4.20126	1.221
4	0.5314	5.20772	1.43

Part 3: As we lifted the ramp higher, we came to a stop at 14 degrees and a height of .29m. With the angle, we were able to conclude that the kinetic friction was 0.249.

Part 4: We raised the ramp at a angle of 25 degree, which is obviously larger than the angle in Part 3. With this angle we see a definite acceleration from the block with the felt on one side of the block. We calculated the kinetic friction to be 0.546 and the acceleration was 0.7106m/s².

Part 5: With the same setup as Part 4, we added a pulley at the top end of the ramp, and a 0.3kg mass weight at one end of the string and the other end of the string was tied to the block which had a mass of 0.25kg; the angle is 25 degrees again. Once the apparatus was put into motion, Logger Pro recorded the motion across a period of time and gave us an acceleration of 1.579 m/s². The theoretical acceleration was 1.259m/s², which gives us a 20% error. The percent error was quite large, but this was due to the small measurements that we took, like the angle and the mass of the block and hanging weight.

Conclusion

To find the static friction and kinetic friction, students must understand the concept of how friction applies. In this lab, we learned that static friction can be measured by using two objects with forces that goes against each other, while the whole apparatus stays completely motionless. Furthermore, kinetic friction can be measured by either the object moving from a force that applies, putting the object in motion, or by two objects with forces that goes against each other, but objects are in motion. This lab required several different methods to measure both static and kinetic friction, and with those measurements, we graphed force applied vs. friction. We also calculated theoretical acceleration, giving us a large percent error. The large percent error was due to inaccurate measurements of the angle or the masses or both.