17-Oct-2016: Lab 15 Collision in two dimensions

1. Title: Lab 15 Collision in two dimensions
    Name: Qiwen Ye (Sherry)
    Lab Partners: Jae Yoo, Chandler
    Date: 17-Oct-2016

2. Purpose
The purpose of this experiment was to look at two dimensional collisions in order to determine if momentum and energy are conserved. 

3. Introduction
We measured the total momentum of steel ball with glass ball and steel ball with plastic ball after a glancing collision and to find the initial and final momentum and energy. At first, we did the experiment about steel ball with glass ball, then we did experiment about steel ball with plastic ball. 

4. Apparatus/Experimental Produce
At first, we leveled the glass table and put the stationary ball on the leveled glass table. Set up a iPhone as the camera on the top of the glass table in order to take a video form aerial view the position of a ball rolling and hit another ball at rest. Aimed the rolling ball so that it hit that side of the stationary ball. Then balls ideally rolled off at some decent angle from one another. After setting up, we inserted the videos into LogPro to analysis the motion trajectory of two balls. Set origin and added point series to record the motion of two balls. Through the LogPro, we opened the Option Menu, Movie Option, choose Override Frame Rate to 60 fps and Advance the movie 2 Frame after adding a new point. 

5. Measured/Graph of Data
Part 1: Steel Ball and Plastic Ball
1) Used the LogPro to describe the motion trajectory of two balls. The blue line was the motion trajectory of the plastic ball; the red line was the motion trajectory of the steel ball. The center line was the motion trajectory of center of mass. 

2) After we recorded the motion trajectory of two balls, we had a lot of points placed on the graph of distance vs. time. Then, used the linear fit to get each lines. The x-direction and y-direction of the ball as separate lines. Used Logger Pro to trace the path of the first ball in each direction, and took the slope of the position before and after the collision, with gave us velocity in the x and y directions. 

3) Used Logger Pro to find the position of the center of mass. Created a new formula in Logger Pro (m1*x1+m2*x2)/m1+m2 to produce the graph:

Xcm vs. t And Ycm vs.t

4) Used Logger Pro to find the velocity of the center of mass. Created a new formula in Logger Pro (m1*v1+m2*v2)/m1+m2:

Vx-cm vs.t And Vy-cm vs. t

Part 2: Steel ball with Glass ball

1) Did the same process as part 1 to record the motion trajectory of two balls. The red line was the motion of glass ball, the blue line was the motion of steel ball and the center line was the center of mass of both balls. 

2) It was the same as part 1, through the graph about distance vs. time, we got the velocities before collision and after collision in x and y direction. :

3) Created a new formula in Logger Pro (m1*x1+m2*x2)/m1+m2 to produce the graph about the position of the center of mass:

4) Created a new formula in Logger Pro (m1*v1+m2*v2)/m1+m2 to get the graph about the velocity of the center of mass:

6. Calculated Data

Used the equation for conservation of momentum in x and y direction to see if momentum before the collision was equal to momentum after the collision. 

Part 1: Steel Ball and Plastic Ball

Part 2: Steel Ball with Glass Ball

Used the equation for conservation of kinetic energy in x and y direction to see if kinetic energy before the collision was equal to kinetic energy after the collision. 

Part 1: Steel Ball and Plastic Ball

Part 2: Steel Ball with Glass Ball

7. Explanation/Analysis

Through the equation of conservation of momentum and kinetic energy, we found that the initial and final momentum and kinetic energy were not equal in those collisions. The different percent of initial and final momentum of the steel and plastic ball was 13.6%, and the steel and glass ball was 15.1%. The different percent of initial and final kinetic energy of the steel ball and plastic ball was 11.2%, and the steel and glass ball was 23.3%. And, we found that the initial kinetic energy was bigger than the initial energy.

8. Conclusion

In this experiment, we determined kinetic energy was not conserved because some of kinetic energy was converted to another form of energy, such as heat; therefore, the kinetic energy was not conserved in those collision. But the total energy was conserved because the initial kinetic energy was equal to the final kinetic energy and the energy of heat. Also, the momentum was not conserved because the net external force on a system was not zero. The glass table that the balls were rolling was not friction less; therefore, it caused the velocity slow down and momentum was not conserved.

12-Oct-2016: Lab Ballistic Pendulum

1. Title: Lab Ballistic Pendulum

    Name: Qiwen Ye (Sherry)
    Lab partners names: Jae Yoo, Chandler
    Date: 12-Oct-2016

2. Purpose
We determined the firing speed of a ball from a spring-loaded gun by using the theorem of conservation of momentum and conservation of energy. Then, we found the distance where the ball hit the ground in order to get the launch speed of the ball by the Newton's Law measurement.

3. Introduction
In this lab, we found the launch speed of the ball by using a spring-loaded "gun" fires a ball into a nylon block, which is supported by four vertical strings. The ball was "absorbed" into the block, and the ball and block together rise through some angle, which measured by the angle indicator shown, on a scale marked in halves of a degree. Through the angle and the length of the string, we found the final velocity both of ball and block that we got the initial velocity of the ball while it was launching.

Assumed that the collision happened so quickly that the strings stay essentially. That way there was no net force on the ball and block system, we used conservation of momentum to write an equation for the speed of the system immediately after the collision. After the collision, the ball and block system rises, losing the kinetic energy and gaining potential energy. At the system's maximum height, its kinetic energy will be zero. Used conservation of energy to relate the maximum height the block reached to the initial speed of the block in order to find the launch speed of the ball.

In order to verify the experimental launch speed, moved the nylon block out of the way and launched the ball with the apparatus on the lab table. Without using the nylon block, we launched the ball from the apparatus outside the lab table, and we verified the distance where the ball hit the ground. Put a piece of carbon paper onto another piece of paper on the ground, close to where we expected the ball to land. Measured the height from the lab table to the ground and the distance, then used below formula to find the how long the ball hit the ground in order to the actual launch speed.

4. Apparatus/Experimental Procedure
Set up the apparatus as shown. Measured the mass of the ball and block and the length of the string; leveled the base of the apparatus. Placed the ball into position and put the angle indicator to zero degrees. Fired the ball into the block and record the maximum angle to which the block rises. Repeated the same progress of four or five time to get an average values.

After this part, we removed the block and launched the ball to the ground from the lab table in order to find the distance that the ball landed. Measured the height of the table and tried to launch the ball in order to place the carbon paper on the ground where close to the distance.

5. Measured Data
m=the mass of the ball
M=the mass of the block
L=the length of the string
Theta=the angle between the string and the origin after collision
H=the height of the table
X=the distance of the ball where the ball hit the ground

6. Calculated Data/Analysis
Used the uncertainties in measurements for the masses and the angle to determine the experimental uncertainty in the launch speed of the ball.

After we verified the launch speed of the ball, we got the actual launch speed is 5.63 m/s. However, our experimental launch speed is 4.73 m/s.

8. Conclusion
In this experiment, we determined the launch speed by two different measurements. One of using conservation of momentum and conservation of energy to find the initial speed. Another one is using the Newton's Law to find the time of  the ball landed and the height of lab table in order to get the initial speed. The different percent of the launch speed is 15.99%. The reason causes the different is the air-resistance, the friction of the string, and the angle indicator not exactly to zero degree.

10-Oct-2016: Lab 13 Magnetic Potential Energy Lab

1. Title: Lab 13 Magnetic Potential Energy Lab

    Name: Qiwen Ye (Sherry)
    Lab partners names: Jae Yoo, Chandler
    Date: 10-Oct-2016

2. Purpose
In this lab, we studied the conservation of energy and determined the relationship between kinetic energy, magnetic potential energy and total energy of the system.

3. Introduction
In order to verify the conservation of energy in the system, we used a friction less cart with a strong magnet on one end approaches a fixed magnet of the same polarity. The carts kinetic energy is momentarily zero and all of the energy in the system is stored in the magnetic field as magnetic potential energy, transformed back to kinetic energy. Because there is no equation for magnetic potential energy that we used the relationship:

About the interaction force F, we used the relationship in the triangle to find that F=mgsina. Here is the example how to calculate the magnetic force.

4. Apparatus
We used a gilder on an air track as our cart on a friction less surface. We provided an angle between the track and the lab table. If we raise one end of the air track the cart will end up at some equilibrium position, where the magnetic repulsion force between the two magnets will equal the gravitational force component on the cart parallel to the track. We used iPhone Compass app to measure the angle to +/-0.1 degree.

5. Measured Data
We did the same experiment five times in different angles, that we measured the angles and distance between magnet r.  And, we measured the cart is m=338 g.

6. Calculated Data

About the magnetic force, we used that equation F=mgsina to get that. m=338g, g=9.8m/s^2, and the angle a is shown above. Therefore, we got five different values of magnetic force by five different angles.

7. Graph

By using the values of magnetic force F and distance between magnetic r, we did the graph of F vs. r. We assume that the relationship takes the form of a power law: F=Ar^n. A=0.0006413, n=-1.517.

A=0.0006413, n=-1.517

Position vs. time

Then, we used the relationship to find the magnetic potential energy:

 After we created the new Calculated Column in LogPro that we got the graph of magnetic potential energy and kinetic energy.

Blue:Total Energy
Purple: Kinetic Energy
Green: Magnetic Potential Energy

8. Explanation

In the graph F vs r, we determined that magnetic force F is decreasing by the distance r become bigger. The total energy is almost a straight line, it means that the energy is conservation. The kinetic energy and magnetic potential energy is opposite, because the conservation energy.

9 Conclusion
In this experiment, we learned the magnetic conservation of energy, which the magnetic energy transform to the kinetic energy. However, the line of total energy goes down shows that some energy disappeared when the cart was going down. The track we used is not exactly friction less, and the air-resistance may cause the energy loss. Overall, this experiment is successful.

05-Oct-2016: Lab 12 Conservation Of Energy - Mass Spring System

1. Title: Lab 12 Conservation Of Energy - Mass Spring System
    Name: Qiwen Ye (Sherry)
    Lab partners names: Jae Yoo, Chandler
    Date: 05-Oct-2016

2. Purpose
In this experiment, we was looking at the energy in the vertically-oscillating mass spring system in order to find the relationship between kinetic energy, gravity potential energy, elastic potential energy and position.

3. Introduction
Amuse the gravitational potential energy is zero at the groud, that we had a uniform spring whose top is held fixed at a height H above the ground. Then use calculus to show that the gravitation potential energy of the spring is mg(H+y)/2. Put our origin at the top of the spring and call downward the positive direction, assume that the spring has a length L, the top of the spring is held at rest but that the bottom end of the spring is moving at a speed v downward. The kinetic energy of the moving spring is 1/2(Mspring/3)v^2.

3. Apparatus/ Procedure
Set up the force sensor, motion sensor, clamps and spring as shown. Opened the LogPro to record the data. Mount the table clamp with a vertical rod to the table. Mount a horizontal rod to the vertical rod. Put a Force sensor on the horizontal rod with the loop of the sensor pointing downward. Then calibrate the force sensor using zero mass and a 1kg (9.8N) weight then remove the weight.

5. Measured Data

The mass of spring is m=89 g.

6. Graph by Prediction

7. Graph by LogPro

KE vs. GPE vs.EPE vs. Postion
Red: Gravitation Potential Energy
Blue: Elastic Potential Energy
Purple: Kinetic Energy
Green: Total Energy

KE vs. GPE vs.EPE vs. Velocity
Red: Gravitation Potential Energy
Blue: Elastic Potential Energy
Purple: Kinetic Energy

8. Conclusion
According to the graph above the GPE became lowest when the EPE of the spring was higher. Also, when the GPE became highest when the EPE of the spring was lowest. The reason was that when the string was fully stretched the mass would have every little gravitational potential energy. Even though the individual reading of graph have giant peaks, the overall sum was relatively staying steady. It shows that the energy is conserved. Some errors may in the accuracy of the reading of the spring constant measurement. And, the height may not be perfectly calibrated with the motion sensor or the spring itself was not perfectly.

05-Oct-2016: Lab 11 Work Energy Theorem Activity

1. Title: Lab 11 Work Energy Theorem Activity
    Name: Qiwen Ye (Sherry)
    Lab partners names: Jae Yoo, Chandler
    Date: 05-Oct-2016

2. Purpose
This experiment is to measured the work done by a spring on a system by stretching a spring through a measured distance and make two graphs about position, force and kinetic energy in order to determine the relationship between work done and the kinetic energy.

3. Introduction
In theory, the work done by the spring should equal to the change in kinetic energy of the cart. We can measure the distance while we stretched the spring to get the work done.

4. Apparatus/Procedure
We set up the ramp, cart, motion detector, force probe, and spring as shown in the picture. Calibrated the force probe with a force of 4.9 N applied. The motion detector sees that the cart over the whole distance of interest - from the position where the spring is just unstretched to the position where it is stretched about 0.6 m.

In order to measure the work done, we used the LogPro to record the movement when the spring is stretched. Opened the experiment file called "Stretching Spring" to display the force vs. position. Then, zero the force probe and the motion detector with the spring supported loosely and unstretched. The motion detector was set to "reverse direction," so that toward the detector is the positive direction.

5. Measured Data
In the LogPro, we began graphing force vs. position as the cart is moved slowly towards the motion detector until the spring is stretched about 0.6 m. Then, we got the graph about force vs. position as shown. Then, we entered the formula KE=1/2mv^2 by using the velocity we got from the experiment and the mass of the cart in order to in order to get the graph of kinetic energy and position.

6. Explanation of Graph

The slope of the graph is the spring constant of the spring that we used, k=8.644 N/m. Because this graph is similar to the y=kx+b. The area of the graph force vs. position is the work done by the spring. Because:

Used the Analyze, Examine to find the change in kinetic energy of the cart after it is released from the initial position to several different final positions by using graph kinetic vs. position. We found that the work done by the spring is equal to its change in kinetic energy. Because the spring potential energy transform to the kinetic energy when we released the spring.

7. Conclusion

In this experiment, the work done by the spring is 0.6655 J; the kinetic energy is 0.556 J. The different percent is 16.4%. The friction between the cart and the track, the air resistance may cause the experiment has that differential. Overall, we determined that the work done of an object is equal to its the change in kinetic energy.

03-Oct-2016: Lab 9 Centripetal Force with A Motor

1. Title: Lab 9 Centripetal Force with A Motor
    Name: Qiwen Ye (Sherry)
    Lab partners names: Jae Yoo, Chandler
    Date: 03-Oct-2016

2. Purpose
In this lab, we studied the rotation motion in order to find the relationship between the angle theta and the angular velocity.

3. Introduction
When an object is rotating like the picture shown, it will provide an angle theta. In order to find the angle theta, we need to measure the length of string, the height from the top to the ground.

4. Apparatus/Experimental produces
We used an electric motor mounted on a surveying tripod and put the long shaft vertically up from the shaft. The horizontal rod mounted on the vertical rod. A long string tied to the end of the horizontal rod. A rubber stopper at the end of the string. A ring stand with a horizontal piece of paper or tape sticking out.

5. Measured Data

We got the relationship between angle theta and angular velocity.  

After that, we did the same experiments in different period (T), that we can get the angular velocity by the equation w=2pie/T (Note: T is in 10 rotation). Also, we measured the height h in order to get the angle theta between the rotation center and the string. 

6. Conclusion

In this experiment, we found that when the angle theta increase, the angular velocity will get bigger. The different percent of angular velocity is between 2.33-8.58%. The reason cause the different is the friction of the apparatus while using the that make a rotation. And, the friction between the string and the rotation point. The air-resistance may also cause the different when the object is rotating.