Group+3

Lab: Rotational Kinematics
Group Members: Brad Barton, Daniel Hong, Jerry Carapolo, Jinhoo Kim Period 2 Completed On: April 6th, 2010 Due On: April 6th, 2010

Objective: To find the relationship between the tangential velocity and the radius of a rotating object. To find the relationship between the angular velocity and the radius of a rotating object.

Procedure: 1. Set up turntable and set radius of the tab on the disc. 2. Turn on the table and record the amount of time that the tab is in the photogate. 3. Do that for different rpms at 4 different radii. 4. Use the time in the photogate to calculate tangential velocity 5. Use that information to calculate angular velocity.

Hypothesis: The tangential velocity is directly proportional to the radius, therefore if the tangential velocity increases the radius will to and vice versa. The angular velocity is inversely proportional to the radius, therefore if the angular velocity increases the radius will decrease. In the equation w=v/r if the radius increases w, the angular velocity, decreases. In the equation v=w*r if r, the radius, increases then the tangential velocity, v, increases.

Materials: Turntable Velcro tab Cardboard disk Ruler Pasco Photogates Laptop



__Graph(s):__

We can see some percent errors due to the experimental errors of the lab. One was measuring the time of the tab within the Photogate timer was done by hand and not at all perfect. We would not hold the timer straight because not only is it very difficult but almost impossible to stay constant. In order to change this lab, I would apply a clamp that would hold the timer above the rotating disk still. A real life application of this lab would be for a DJ, who uses many turntables at one time to create the effects that he would want using various rpms and essentially create music.

Sample Calculations (Trial 1 of 16 RPM)

Tangential Velocity v=d/t v=.02/.063 v = 0.317m/s

Angular Velocity w=v/r w=.317/.179 w=1.768 rad/s

Theoretical Tangential Velocity v= rpm * 2 * π * r / 60 v = 16 * 2 * π * .179 / 60 v = 0.30m/s

Percent Error Percent Error = (ltheoretical-actuall)/theoretical *100 Percent Error = (.30-.317)/.30 * 100 Percent Error = 5.67%

__Evaluation/Conclusion:__ Our hypothesis made before the experiment was correct for both cases. In our data, when we increased the radius the tangential velocity also increased. This is because the velcro tab has to travel more distance when the radius is larger in the same amount of time as the velcro tab when it has a smaller radius. When we increased the radius from .140m to .179m the tangential velocity increased from .216m/s to .317m/s. Our second hypothesis also proved to be correct because when the angular velocity increased the radius decreased as is seen in our data. In our data when the radius was increased from .140m to .179m the angular velocty decreased from 1.867rad/s to 1.768rad/s.

__Analysis__: 1. As the radius increases tangential velocity also increases. For example, in the 16 rmp category, when the radius was .14m, the tangential velocity was .261 rad/s. And when the radius increased to .179m, the tangental velocity increased to .317 rad/s. 2. Theoretically, as the radius increases the angular velocity should stay the same. However, due to error, the angular velocities didn't remain constant and didn't follow a pattern. 3. The slope equals the angular velocity for each turntable speed setting. The equation for tangential velocity is V=r**ω.** The radius represents the x axis and the tangential velocity represents the y axis, so the angular velocity is the slope. 4. There will always be human error when using stopwatches and that is how you would need to measure the period. We are able to ensure less error when using the photo gate timer. We can also just use the equation and find the angular velocity with the slope instead of other equations. 5. The reason we use angular qualities is because linear velocity measures the speed in linear units while the angular velocity allows us to measure the velocity of an object in a circle and the time it takes to get around a certain amount of angle. Linear velocity can not do that.

Lab: Ballistic Pendulum
Group Members: Dan Hong, Jerry Caropolo, Brad Barton, & Jinhoo Kim


 * Objective:** Solve for the initial velocity of the steel ball that is launched from the launcher, derive it from two different methods- work energy and projectiles, and compare the two results.


 * Hypothesis:** The initial velocity of the steel ball that is found with the projectile method should be congruent with the velocity that was found using the wok energy method.


 * Procedure**
 * Part 1-Using Projectile Motion**
 * 1) Set up launcher to be perfectly horizontal. Place on table and set to medium range.
 * 2) Lay out a sheet of white paper under carbon paper in the approximate area where the ball will land on the floor. Measure the Δx value or range of the projectile by firing ball five times, each time recording the distance from the launcher to the in meters.
 * 3) Measure the Δy value by recording the height of the launcher to the floor.
 * 4) Use the Δy value and kinematics to solve for time in the air. Use the time value and the Δx value to solve for initial velocity.


 * Part 2- Using Work, Energy, and Momentum**
 * 1) Record the masses of the steel ball and the ballistic pendulum in kilograms. Measure the length of the pendulum from the top to the line indicating center of mass.
 * 2) Load the ball to medium range and fire five times, each time recording the angle in degrees. After the first trial, move the angle lever slightly back, so as to limit the effect of friction on the reading.
 * 3) Using trigonometry, solve for the height from the horizontal where the pendulum hangs, to the highest point the pendulum reached. Subtract this value from the total (the value measured earlier from the top of the pendulum to the center of mass) to acquire the distance from the highest point to zero.
 * 4) Plug in this height value into the Work Energy formula. Solve for velocity.
 * 5) Using the Conservation of Momentum equation, solve for initial velocity.

Sample Calculations (for average of displacement of Projectile and Trial 1 of Work Energy) Mass of steel ball: 0.066 kg -> M1 Mass of Pendulum: 0.311 kg -> M2 Length of Pendulum from the center of mass: 0.2725 meters Angle measure: 42.5

__Projectile Method__ ∆x= 2.025 meters ∆y= 0.820 meters ∆dy= visinøt + 1/2at^2 -0.82=(.5)(-9.8)t^2 t=0.409

∆dx = vit 2.025=vi(0.409) vi=4.95 m/s

__Work Energy Method__ Ke=PEg 1/2(m1 + m2)v^2= (m1 + m2)gh v = √2gh m1v1 = (m1 + m2)v' m1v1 = (m1 + m2)√2gh v1= (m1 + m2)√2gh/m1 v1= (0.066 + 0.311)√2*9.8*0.089212/0.066 v1 = 7.55 m/s

h= 0.275- 0.275*sin(42.5) h=0.089212 meters

1.In general, what kind of collision conserves kinetic energy? What kind doesn’t? What kind results in maximum loss of kinetic energy?
 * Discussion Questions

2.Consider the collision between the ball and pendulum. a.Is it elastic or inelastic? b.Is energy conserved? c.Is momentum conserved?

3.Consider the swing and rise of the pendulum and embedded ball. a.Is energy conserved from the moment just before the ball strikes the pendulum to the moment the pendulum rises to its maximum height? b.How about momentum?

4.It would greatly simplify the calculations if kinetic energy were conserved in the collision between ball and pendulum. a.Calculate the loss in kinetic energy as the difference between the kinetic energy before and immediately after the collision between ball and pendulum. b.What is the percentage loss in kinetic energy? Find by dividing the loss by the original kinetic energy. c.According to your calculations, would it be valid to assume that energy was conserved in that collision? d.Calculate the ratio M/(m+M). Compare this ratio with the ratio calculated in part (b). Theoretically, these two ratios should be the same. State the level of agreement for these two quantities for your data.

5.Go to http://www3.interscience.wiley.com:8100/legacy/college/halliday/0471320005/simulations6e/. Select “Ballistic Pendulum” from the column on the left. What is the effect of increasing the mass of the ball? What is the effect of increasing the pendulum mass? Try it. (NOTE: You have to read “Student Notes” first before you can run the simulation.)

6.Is there a significant difference between the two calculated values of velocity? What factors would increase the difference between these two results? How would you build a ballistic pendulum so that momentum method gave better results?**

__**Work Done by Friction**__
By: Jerry Caropolo, Brad Barton, Dan Hong, & Jinhoo Kim Period 2 Completed on: Due on: February 9th


 * __Objective__:** To find the relationship between initial kinetic energy and the amount of work done by friction.


 * __Hypothesis with Rationale__**: The initial kinetic energy and the amount of work done by friction will be equal and opposite. This is because it will take the same amount of energy to stop the object in motion as it did to start it. Also, in order for the friction to slow and eventually stop the object, it must be acting on the same axis in the opposite direction.


 * __Materials__**: Wooden block,10 meter tape measure, string, force sensor, Data studio, motion sensor, scale

1. Set up force sensor. Open data studio. 2. Measure the coefficient of kinetic friction between the floor and the wooden block 3. Throw block down the hall 4. Record displacement and initial velocity of the wooden block 5. Repeat experiment 3-5 times
 * __Procedure__**:

__Task A:__



Wooden block's Data

Work and Kinetic Energy calculations

__**Sample Calculations**__(Trial 1)

Normal Force
 * [[image:Picture_14.png]]

Work

Kinetic Energy **

Force of Friction

Percent Difference

__**Conclusion**__

Based on our data and calculations, our experiment was successful. Our hypothesis, which states that our values for initial kinetic energy and work due to friction will be equal and opposite, was successful. This is because we achieved relatively close values for these two during most trials; this is shown in our percent difference values. This makes sense because the block stopped due to the work being done by the friction between the floor and the bottom of the block, so the magnitudes should be equal but the direction on the x-axis should be in the opposite direction.

__Task C__: __V vs T Graph__

Our average kinetic energy in this lab was .645J and our average work was .778J. The percent difference in this experiment 17.1%. This percent difference is rather big, which results in our were not accurate at times. Our largest percent difference was 28.5% and our smallest was 11.4%. This shows that some errors must have affected our results.

One of the errors could have occurred from the starting point we threw the block from. We had to use our judgment to start at the same location every time we threw the block. This would have affected the distance traveled by the block and in the end change our results. To fix this error we could have marked where we would throw the block by a piece of tape. Another source of error could have come from obtaining the kinetic friction force. Each time we pulled the block it was not perfectly horizontal and we did not pull it by the same force each time. Another source of error could have occurred from inconsistent throwing of the block. Every time we threw the block it was never with the same force. The distance traveled, velocity initial, and all of our calculations were different each time. To fix this problem we could have had a type of launcher that would shoot the block consistently with the same amount of force each time. Another source of error is measuring the distance traveled by the block. We had to use our eyes to figure out how far the block traveled so our calculations and results may be off. We could have used another ruler to obtain the precise distance traveled to the appropriate amount of significant figures. These errors are all human errors, which could have been avoided with the appropriate materials.

1. How does the magnitude of Work compare to the kinetic energy? The magnitude of Work done by friction is equal to the kinetic energy of the wooden block.

2. How do you explain the relationship between the Work Done and the Kinetic Energy? The relationship between the Work Done by friction is equal but negative to the Kinetic Energy of the wooden block.

3. What do you think would happen if you used a block with more mass? If we used a block with more mass, I think that the work done by friction would increase. Since friction is equal to the Normal Force times the coefficient of friction, and the Normal Force is equal to the weight of the block in this case, increasing the mass of the block would increase the normal force of the block and increase the Work done by friction.

4. What do you think would happen if you used a rubber block instead of a wooden block? If we used a rubber block instead of a wooden block, the work done by friction would increase dramatically. The rubber to the floor has a greater amount of friction and when thrown at a certain initial velocity, it would have a smaller displacement than a wooden block thrown at a certain initial velocity. The factors that stays constant when changing the material of the block are the initial and final velocity, and the mass of the block.

5. What do you think would happen if you did this experiment on ice instead of on the tile floor? Doing this experiment on ice would create an incredibly sharp decrease in the work done by friction because the block would have a greater displacement over time with the same negative initial and final velocity.

In this lab, there are much room for error. Some errors are not throwing the block at the same initial velocity and not having the block end in the same position. I would change the lab by having a horizontal launcher so that the initial velocity stays constant and that we have consistent results. Since the block was thrown in any manner, it did not travel a straight path so the motion sensor could not accurately detect the block every trial. Finding the displacement of the object was also not completely accurate because we used our judgment to see the block's final position. Instead of depending solely on the motion sensors, all of the members of my lab group could have used stop-watched timers in order to obtain a more congruent time to the acceleration. One of the applications that is relevant to this lab is that many car companies and tire companies because in order to ensure the customer's safety; they must make the safest and most durable tires. They want to make tires with the greatest coefficient of kinetic friction so that if a car is moving very fast it can come to a safe stop because it will have higher initial kinetic energy than a tire with a lower value for coefficient of kinetic friction.

**Lab: Energy of a Projectile Launcher**
By: Jerry Caropolo, Brad Barton, Dan Hong, & Jinhoo Kim Period 2 Completed: 2/22/10 Due: 2/22/10

__Objective:__

In this experiment, we want to find the relationship between the potential elastic energy before the launch, the kinetic energy at the moment of the launch, and the potential gravitational energy at the apex.

__Hypothesis__:

When launched from a launcher, a ball will have the same maximum potential elastic energy, maximum potential gravitational energy, and maximum kinetic energy. Before being launched, there is only potential elastic energy. This is the maximum potential elastic energy. Once launched, the potential elastic energy will immediately change into the maximum kinetic energy because the ball is traveling at it's fastest velocity. At the apex, the velocity will be zero, and the ball will be at it's highest point, therefore, all of the kinetic energy will be transferred into potential gravitational energy.

__Materials:__ Projectile Launcher, Plastic Ball, Motion Sensor, Meter Stick, Masses, Tape, Plastic Cup, Ram Rod, Caliper, Photogate, Clamp, Photogate clamp

__Procedure:__ (Steps 6 and 7 were substituted with Mrs. Burns's data.)
 * 1) Clamp the Projectile Launcher on to the table.
 * 2) Set the launcher straight up towards the ceiling at a 90 degree angle
 * 3) Tape the Motion Sensor directly above the launcher
 * 4) Launch ball five times, recording time in gate and distance traveled.
 * 5) Calculate initial velocity from photogate data.
 * 6) Tie cup to rod and place inside barrel.
 * 7) Add mass to cup, converting mass to weight and measuring the displacement of the spring.

Potential Energy:

Sample Calculation for Potential Energy (Trial 1)

Kinetic Energy:



Sample Calculation for Kinetic Energy (Trial 1)



Spring Force Constant (Trial 1):



__Calculation for Potential Elastic Energy__



__Percent Differences__

PE e and KE

PE e and PE g

KE and PE g

__Discussion Questions:__

1. Why didn't we calculate Work due to spring or due to gravity? We did not need to calculate Work due to spring because it was already included as the PEs. Work due to gravity is already included as the PEg.

2. How do you explain the relationship between PEs, PEg, and KE? The total energy of the system is the same throughout because the law of conservation of energy states that energy can not be created nor destroyed. Therefore, the energy in the system is always constant. The energy in this case is transformed multiple times. When the ball is pushed into the launcher and at rest only PEs is present. Once the ball is launched the PEs is transformed into KE. Once in the ball is in the air and at its maximum height the KE is transformed into PEg. The values are all equal because at every given point the total amount of energy in the system must be equal because of the law of conservation of energy.

3. What do you think would happen if you used a ball with more mass? If we used a ball with more mass all of the values of energy would be increased, therefore the total energy of the system would also be increased.

__Evaluation/Conclusion:__ Our hypothesis was most correct when comparing gravitational and elastic potential energy. This relationship had the least percent difference. The two values were .094 and .082 respectively. Also, that percent difference was 13.54%. The other two relationships had higher percent differences. Potential gravitational and kinetic energy had a 26.1% difference and kinetic and potential elastic had a 39.3% difference. This can lead us to believe that most of the error happened in the data collection of the kinetic energy. All of the possibilities for error are covered later in the conclusion. To address the errors in the lab I would have changed the lab several ways. First we could have used a better method to obtain the force needed to push down the spring, therefore finding a more accurate spring force constant. Then we would have had a different PEs. If possible we could have had something to launch the ball with a constant force or maybe a different launcher that always launched the ball with a constant force.. Then all of our values of PEg and KE could have been closer together. All of the errors made in this lab was human error, which could have been fixed with the right materials. Conclusion Part 2-Error In this lab, we were looking to find the relationship between the elastic potential energy of the spring, the kinetic energy right when the ball is launched, and the potential energy at the maximum height of the ball's trajectory. We know that all of these values should be the same, because energy cannot be created or destroyed according to the Law of Conservation of Energy. In this sense, as the potential energy of the ball decreases, the kinetic energy should increase and vice-versa. Our value for Potential Spring Energy, Initial Kinetic Energy, and Gravitational Potential Energy at maximum height were .0826J, .123J, and .0945J respectively. Theoretically, these three values should have been the same but because of the error experienced during the lab they were off. Some possible sources of error include the condition of our spring, the distance between the true initial position of the ball and the photogate, and the way we measured the maximum height of the ball. For the first part where we recorded the Potential Spring Energy, we used a spring force constant based on the data we received from Mrs. Burns’s trials. Our value possibly could be different, depending on the age and condition of our spring. If so, this would have resulted in a larger or smaller Potential Spring Energy value. For measuring the Initial Kinetic Energy we used a photogate above the barrel of the launcher; the fact that the photogate was not exactly at the ball’s initial position also threw off our data. Lastly, our value for the Gravitational Potential Energy was also off since we used a motion sensor taped to the ceiling as our measuring tool, subtracting the distance from the sensor from the total distance between the sensor and the cannon. Because we were relying on the accuracy of the sensor and had to deal with a ball trajectory that was not always on the same vertical axis, our measurements here would have been different as well.

A real life application of this would be when trying to launch a projectile vertically to a desired height. For example, a circus performer being launched straight into the air through onto a platform. All of the constants will have to be carefully calculated so that the launch will work and will be safe. They will have to adjust the spring to the desired amount. They will also have to adjust the length of the cannon in order to reach the desired velocity. Then you will be able to calculate how high the performer will be launched into the air and then place the platform on the desired height.