10/17/2016 : Collisions in Two Dimensions

Lab #15: Collisions in Two Dimensions

Name:    Charles Xu,

Partner:  Anthony, Michell

Date:      10/17/2016

Statement:

In this experiment, the purpose is to determine if momentum and energy are conserved. We used three different balls, two with the same mass, and the other with smaller mass. 

Summary:

First, we level the glass table so that the ball can be at rest before the collisions. Second, we measure the width of the edge of the glass table so that we are able to set scale later on. 

Third, we set up a smart phone above the glass table and recording videos of collisions in slow motion. Then we use a heavier ball to collide the lighter one at the center. 

Setup for Collision Experiment 

After recording video, we used logger pro to collect data from the videos. 

Data Points for Different Masses Collision

Data Points for Same Mass Collision

We set origin on the video and adjust the x axis so that it lines up with the trace of moving ball before collisions. Then we use add point series to add columns relate to center of mass. 

Then, we plot X center of mass and Y center of mass vs. time graph and velocity of center of mass in x direction and velocity of center of mass in y direction vs. time graph.

X center of mass and Y center of mass vs. time graph (different masses)

X center of mass and Y center of mass vs. time graph(same mass)

 velocity of center of mass in x direction and velocity of center of mass in y direction vs. time graph.(different masses)

velocity of center of mass in x direction and velocity of center of mass in y direction vs. time graph. (same mass)

Energy Conserved

For the calculation, I choose two sets of data. One is the velocity of center of mass at both x and y direction before the collision. The other is the same type of data but after collision. KE = ½m(Vx^2+Vy^2). I plug in the sum of two balls' masses as m, then plug in velocity of x direction and velocity of y direction as Vx and Vy. After calculating both before the collision and after collision, i found that the total energy is almost the same. The difference might occur because of friction.

For calculation the momentum, i use the same data sets as the calculation for energy. I got two numbers that are very close, which means that the momentum conserved in this collision.

Conclusion:

By doing this experiment and the calculation, we find that the momentum and energy were conserved in this collision. In the calculation, there is some difference between initial momentum, energy and final momentum, energy. The possible reason is that we didn't have the perfect data from the video by clicking frame by frame. Another possible reason is the friction between balls and glass. 

10/05/2016 : Conservation of Energy - Mass Spring System

Lab #12: Conservation of Energy - Mass Spring System

Name:    Charles Xu,

Partner:  Anthony, Michell

Date:      10/05/2016

Statement:

In this experiment, we set up the vertically-oscillating mass-spring system, and using logger pro, motion sensor, and force sensor to collect datas. Then we compare Kinetic Energy, Gravitational Potential Energy, Elastic Potential Energy, and Total Energy.

Summary:

For this experiment, we set up out mass-spring system with the spring we used for lab #11, so that we are able to have the spring constant. Instead of using 250 grams hanging mass, we used 1 kg hanging mass. We stretch the spring and then release it with the motion sensor collecting datas. Then, using logger pro we plot position vs. time and velocity vs. time graphs. 

Setup of Mass-Spring System

Position vs. Time graph and Velocity vs. Time graph

As the result, we got two sin waves as the graphs. Later on, we added four more calculate columns, which are Kinetic Energy column, Gravitational Potential Energy column, Elastic Potential Energy column, and Total Energy column. Then we plot KE vs. position graph, KE vs. velocity graph, GPE vs. position graph, GPE vs. velocity graph, EPE vs. position graph, and EPE vs. velocity graph using logger pro.

KE vs. position graph, KE vs. velocity graph

GPE vs. position graph, GPE vs. velocity graph

EPE vs. position graph, EPE vs. velocity graph

and last step, we plot KE, GPE, EPE, Esum vs. position graph and KE, GPE, EPE, Esum vs. time graph.

KE, GPE, EPE, Esum vs. position graph and KE, GPE, EPE, Esum vs. time graph.

Conclusion:

By the conservation of energy, the total energy should stay as constant. However, in this experiment, we have the total energy as decreasing function. To explain the error, I think the elastic potential energy and gravitational potential energy not only convert into Kinetic energy but also some work done by the air resistance. This is one of the reason why the sum of energy is decreasing. 

10/12/2016 : Ballistic Pendulum

Lab #14: Ballistic Pendulum
Name:   Charles Xu,
Partner: Anthony, Michell
Date:     10/12/2016

Statement:

For the purpose of this experiment is to find the firing speed of a ball from a spring-loaded gun.

Summary:

In this experiment, we use the spring-loaded "gun" fires a steel ball into a nylon block, which is supported by strings. We measure the mass of the steel ball, mass of the block, and length from top of the spring to the center of the block before the experiment. Then we fire the ball four times at the same notch and record four angles. Then use the uncertainties in your measurements for the masses, length, and angles to determine the experimental uncertainty. 

Setup for the Experiment with Spring-Loaded Gun

Measurements for Experimental Data

Calculation Done to Find the Propagated Uncertainty of the Firing Speed

Calculation for Estimate Distance

From the calculation, we estimate the distance that the ball will travel in x direction if we fire the ball from the edge of the table. We place a piece of carbon paper on top of the other piece of paper on the ground, then fire the ball from the edge of the table. Turns out we have the perfect match. We have 2.3 meters as measurement, 2.3 meters for calculation.

Conclusion:

Comparing the calculation to our verification, we have a successful experiment. We successfully calculated the firing speed of the spring-loaded gun at first notch. The important thing to notice is that the length of the radius should be the top of the string to the middle of the block. I think it would affect the answer if was done incorrectly.

10/10/2016 : Magnetic Potential Energy

Lab #13: Magnetic Potential Energy
Name:   Charles Xu,
Partner: Anthony, Michell
Date:     10/10/2016

Statement:
The purpose of this experiment is to verify that magnetic potential energy and kinetic energy are conserved.

Summary:
Unlike gravity potential energy or elastic potential energy, we have equation, we don't have an equation for magnetic potential energy. In order to accomplish this experiment, the first step we have to find an equation for magnetic potential energy. To do so, we first level the air track and measure the separation of the magnetic when the glider is at rest. Then, we raise the air track to multiple angles and collected different separation. As the air track goes steeper, the separation becomes smaller. We using the theory that magnetic force will equal to gravitational force component parallel to the track. Then, we use power fit to find the A and n for the function of F=Ar^n.

Force vs. r graph

From the curve fit we have our A value as 0.0004724, and n value as -2.004. Then we take the integral of the negative force function and we have our magnetic function. 

After we have the equation of the magnetic force, we place the air track back to horizontal. We give a little push to the glider so that it can go toward the magnet and pushed back by the magnetic force without contacting with the magnet. We measure data with motion sensor and plug in datas. Then we plot Magnetic Potential Energy vs. Time graph and Kinetic Energy vs. Time graph.

Magnetic Potential Energy vs. Time graph and Kinetic Energy vs. Time graph

From the graphs, we can see that when magnetic potential energy increases, kinetic energy decrease. As time goes by, the total energy remain almost the same. 

Also, we plot the Position vs. Velocity graph.

From this set of graphs, we could tell when the glider got to the point that pushed backward by the magnetic force. 

Conclusion:

As the datas and graphs shown, velocity decreases as the glider is getting closer to the magnet. The magnetic potential energy increases when the glider is getting closer to the magnet. Therefore, kinetic energy of the glider decreases when the glider is getting closer to the magnet. From the Magnetic Potential Energy vs. Time graph and Kinetic Energy vs. Time graph, we could tell magnetic energy and kinetic energy are conserved.

10/05/2016 : Work-Kinetic Energy Theorem

Lab #11: Work-Kinetic Energy Theorem 

Name:    Charles Xu,

Partner: Anthony, Michell

Date:    10/05/2016

Statement:

In this experiment, we comparing the measurement of work that was done and kinetic energy that recorded, and find the relationship between this two sets of datas.

Theory:

This experiment was divided by two parts. We need to find the relationship between work and kinetic energy using force sensor and motion sensor.

Summary:

In the first part of the experiment, we pulled a cart on the track, which was attached to the spring. Then we use force sensor to measure the force when the spring was stretched to a certain amount of distance. Then plot the Force vs. Position graph using LoggerPro. Then used linear fit to find out the function for the graph. The slope of the function is the spring constant we looking for. In our experiment, which is 13.64 N/m. Then using the integration routine in the software, we were able to find the work done by stretching the spring 60 cm. We got 2.248mN as result.

This is the set up for the Experiment

For the set up, we have a cart with a force sensor on it. On one end, there is a white board that attached on the cart by magnet. It allows motion sensor detects the cart easier. On the other side, a spring is attached on the force sensor. The book beneath the spring is to reduce experimental error by keeping the spring not stretched. 

The analysis graph in LoggerPro

For the second part of the experiment, we use the same spring so that we have the same spring constant that we have measured in part one. We pull the cart to the same spot as part one, which is 60 cm apart from the initial position. This time we release the cart and let motion sensor to measure the datas. From the collected data, we plot Force vs. Position graph and Kinetic Energy vs. Position graph. In order to have beautiful graphs, we use strike through data cells method to remove useless data points on the graphs. 

Force vs. Position graph and Kinetic Energy vs. Position graph

Here are the Force vs. Position graph and Kinetic Energy vs. Position graph. This two graphs look like opposite to each other from looking at the graphs. Furthermore, we select a portion of datas and use examine feature of the software to compare two datas.

Examine 

We select a data point on the graph, for the first graph, we have the area as 1.64mN; for second graph,

we have kinetic energy as 1.535J. Comparing this two numbers, there are almost identical.

Conclusion:

From this experiment, we could say that the work done by pulling the spring almost identical to the kinetic energy that the cart has after releasing. In my opinion, the work done by pulling the spring converts to elastic potential energy of the spring, then elastic potential energy converts to kinetic energy and heat. The little difference between the Work and Kinetic Energy is converted to heat produced by friction. 

10/03/2016 : Centripetal Force with a Motor

Lab #9: Centripetal Force with a Motor
Name:   Charles Xu,
Partner: Anthony, MichellDate:     10/03/2016



Statement:
In this experiment, we want to find a relationship between θ and ω using a spinning motor.

Theory:
Find the relationship between Force and angular speed. Then using trig to substitute Force to θ with known values.

Summary:
Here is the set up of the Motor

We used the meter stick to measure the height of the spinning rod on the top of the motor to the ground and the length of the string. Then, we measure the distance between horizontal rod and the floor, when the stopper just hits the top of the paper on the rod. According to the data, we could find the distance between two horizontal rods, and calculate the angel θ using tangent. We also measure the time period that the motor spins ten rotation before we setting up the ring stand. 

Data from Measurement

Another step, we use free body diagram to rewrite net force equation in terms of gravity acceleration, radius, θ and ω. 

For the radius in the equation, it equals to R(length of the rod from the center) +L(length of the string)sinθ

Then we input our datas into excel and calculated ω using the equation we found, and compared with the ω calculated from time method.

Conclusion:

By comparing the ω calculated from the equation we found to the ω calculated using time, we could found that these two sets of numbers are very close. Therefore, we could say that the relationship between  θ and ω is the equation we calculated. ω=sqrt(g*tanθ/r).

09/28/2016 : Centripetal Acceleration vs. Angular Frequency

Lab #8:  Centripetal Acceleration vs. Angular Frequency
Name:   Charles Xu,
Partner: Anthony, Michell
Date:     09/28/2016

Statement:
We use the rotating disk to find the relationship between Force, Radius, and Angular Speed by varying masses, radii, and voltage. 

Theory:
1st: If radius increases, force will increase, and angular speed omega will increase;
2nd: If Voltage increases, which will increase angular speed omega, therefore, force will increase;
3rd: If mass decreases, force will decrease, and angular speed omega will decrease.

Summary:
Here is the set up of the electric rotating disk.

For the first experiment, we set mass to be 200 grams and Voltage to be 6.1 volts. Then we varied radius from 19 cm to 28.5 cm, 40cm, and 54cm. We collected data from Logger Pro. 

Data for Experiment #1

For the second experiment, we still set the mass to be 200 grams and radius to be 54cm, but this time we were varying the voltage from 6.1 volts to 6.6 volts, 7 volts, and 7.7 volts.

Data for Experiment #2

For the third experiment, we set the radius to 54cm and voltage to 7.7 volts. This time, we varying the masses from 200 grams to 100 grams, and 50 grams.

Data for Experiment #3

Conclusion:

From the first set of experimental datas, we found out that when radius increases, the force the sensor detected increases. 

From the second set of experimental datas, we found that when voltage increases, it increases the angular speed and the force.

From the third set of experimental datas, we found that when the mass decreases, the force decreases as well.

09/21/2016 : Modeling Friction Forces

Lab #7: Modeling Friction Forces
Name:   Charles Xu,
Partner: Anthony, Michell
Date:     09/21/2016

Statement:
We did five experiments involving static friction or kinetic friction. We derive equations and collect data and capture the graphs to find coefficient friction

Theory:
This experiment we have five different sets of experiment. First, we want to find the coefficient of static friction between block and table using logger pro. Second, we want to find the coefficient of kinetic friction between the block and table using logger pro. Third, we want to find the minimum angle that will cause the block slices off the inclined. Fourth, we use logger pro motion sensor to measure the acceleration of the block when slices of an inclined at some specific angle. Fifth, we use logger pro motion sensor to measure the acceleration when hanging mass pull the block on the flat surface. 

Summary:
First:
We set up a pulley at the edge of the table. On the left side, we have a block on a flat surface; on the other side, we have a hanging mass on the pulley. We added 5g each time on the hanging mass until the block starts to move. This experiment allows us to find the static friction, which leads us to the coefficient of the static friction. We measure the weight of each block, and we added on block each time during four experiments. Then we plot the datas into logger pro, it provides us a linear fit graph. From the logger pro analysis, we have our coefficient of static friction as conclusion.

The graph after we plot points 

The setup for the first experiment

Second:
We connected the force sensor into logger pro. In this experiment, we pulled different numbers of blocks and recorded different forces. In order to make the experiment data more accurate, we calibrate with a 500-gram hanging mass. We use logger pro to analysis data and found the slope of each graph is coefficient of kinetic friction.

Set up for the second experiment

Time vs. Force graph

adjusted graph for second trail.

Third:
For the third experiment, we simply place the block on the horizontal surface. Then, slowly lift up the surface until the block starts to slice down. Next, measure the angle of the surface. Following, we use the angle we just measured and calculated the coefficient of static friction.

Setup for the third experiment

Calculation for coefficient of static friction

Four:

The fourth experiment is to set up a block on an inclined surface, then use the motion sensor to detect the acceleration of the block.

Acceleration graph and velocity graph 

calculation for coefficient of kinetic friction

Fifth:

The last experiment is use the coefficient of kinetic friction that found in part 4 to derive equation and calculate the acceleration.

calculation for acceleration

Conclusion:

The first two experiments, we measure variables according the basic friction formula to find the coefficient of friction. There might be human error when we adding weight for the first experiment. We might add more force to the system when we adding mass. For the second experiment, we had error when we were doing the second trial. We pulled more mass but recorded with less force, which didn't make sense. Later we redo the trail, and fortunately, we were able to fix the error. For the third and fourth experiment, we taped the phone on the surface, therefore, we could have more accurate measurement when we tilted the board.