Group+6

(ASACDWS) William Fassuliotis, Tony Greco, Alex McCullough, Tony Xu

__Due: 4/7/10 Completed on: 4/6/10 Period 6__ =Lab 19: Rotational Kinematics= Tony Greco: Task A Alex McCullough: Task B Steph Cha: C or D

Photogate, Turntable, ruler, marker, disc, data studio

Tangential Velocity
= d/t =0.019/0.0121176 =1/5679 m/s

Theoretical Angular Velocity = (rpm) (2π)/60 =(16) (2π)/60 =1.6755 rad/s Percent Difference = 100(actual-theoretical)/(actual) =100(1.6755-1.8465)/(1.6755) =9.2599%
 * RPM || Theoretical Angular Velocity (rad/s) || Angular Velocity (rad/s) slope of the graph || Percent Difference ||
 * 78 || 8.1681 || 8.7365 || 6.5056 ||
 * 45 || 4.7124 || 4.6019 || 2.4009 ||
 * 33 || 3.4558 || 3.4025 || 1.5651 ||
 * 16 || 1.6755 || 1.8465 || 9.2599 ||

__Discussion Questions:__
1. What happens to tangential velocity as the radius increases? Tangential velocity and the radius are directly related. Therefore, as the radius increases, tangential velocity increases also, resulting a positive linear slope. 2. What happens to angular velocity as the radius increases? Since the angular velocity is depended on the size of the angle, the angular velocity stays constant as the radius increases. 3. What does the slope of each line indicate? The slope of each line indicates the angular velocity (radians/sec). 4. Why didn’t we measure the velocity by measuring the period and circumference? If we measured the velocity by measuring the period and circumference, it would result an average velocity. But, for this lab, we need the instantaneous velocity, not the average velocity. 5. Since we can convert everything to linear anyway, what you suppose is the point in using angular quantities? When we use angular quantities, we are able to observe different perspectives of the object. That’s why we use angular quantities so we don’t always have to know only the translational motion

Conclusion:
Through this lab, our purpose was satisfied and our hypothesis was correct. We were able to find the relationship between tangential velocity and radius; radius and angular velocity in radians. As radius increases, tangential velocity increases because according to the equation, radius and tangential velocity are directly related. For example, when the radius was 0.122 m, the tangential velocity was 0.98 m/s. Then when the radius decreased to 0.182 m, the tangential velocity = 1.57 m/s. But as the radius increases, angular velocity stays the same because the angle is not affected by the change in radius. The angular velocity is only changed by the different rpms. For example, when the RPM=16, the angular velocity=1.84fad/s. Then when the RPM increased to 33, angular velocity = 3.4025. Therefore, as radius increases, tangential velocity increases and angular velocity is not affected.

= = Due 3/25/10 Period 6

Tony Xu: Task A Alex McCullough: Task B William Fassuliotis: Task C Tony Greco: Task D =**Ballistic Pendulum Lab**=

__Objective__: Find the relationship between initial and final momenta of a ball fired into a ballistic pendulum.

__Hypothesis__: The initial momentum of the ball into e ballistic pendulum will be equal to the final momentum of the ball into the ballistic pendulum because the masses of the ball will remain the same, and the initial velocity will be equal to the final velocity (right after the collision) due to the Law of Conservation of Momentum.

__Materials__: Projectile Launcher and steel ball, Plumb bob, meter stick, 2 photogate timers and bracket, Smart timer, C-clamp, Mass Balance, String, Ruler.

__Procedure:__ 1. Mass both the steal ball and the pendulum 2. Find velocity using two different methods 3. First place carbon paper in front of the launcher to find the exact distance the ball traveled with the launcher set to the highest speed, and using the theoretical time to hit the ground, calculate the velocity 4. Next set up the pendulum in front of the launcher and once again se the launcher to the maximum speed. 5. With the angular detector in front of the swing, and then launch, and observe the angle, it will not be at its highest point, because of friction of it on the end. 6. Then shoot it again and again until you can get the exact angle that the ball swing travels each time. 7. Use this angle to help calculate the Velocity of the ball, and the momentum initial and final of the ball.

__Set up__:

__Data Tabl__e: Ball Launched as Projectile Data Ball Launched Into Ballistic Pendulum Data
 * Trial # || Mass of Ball (kg) || Distance (m) || Height (m) || Travel Time (s) || Veolicty (m/s) ||
 * 1 || 0.066 || 2.998 || 0.885 || 0.424984994 || 7.054 ||
 * 2 || 0.066 || 3.018 || 0.885 || 0.424984994 || 7.101 ||
 * 3 || 0.066 || 3.076 || 0.885 || 0.424984994 || 7.238 ||
 * 4 || 0.066 || 3.032 || 0.885 || 0.424984994 || 7.134 ||
 * 5 || 0.066 || 3.004 || 0.885 || 0.424984994 || 7.068 ||
 * Average || 0.066 || 3.0256 || 0.885 || 0.424984994 || 7.119 ||
 * Trial # || Mass of Pendulum (kg) || Angle Created (degree) || Initial Height of Pendulum (m) || Final Height of Pendulum (m) || Change in Heigh of Pendulum (m) || Final Potential Energy (J) || Initial Velocity of Pendulum and Ball (m/s) || Initial Velocity of Ball (m/s) || Initial Momentum of Ball (kg*m/s) || Final Momentum of Ball (kg*m/s) || Percent Difference (%) ||
 * 1 || 0.247 || 56 || 0.295 || 0.1651 || 0.1299 || 0.3985 || 1.5957 || 7.5677 || 0.4995 || 0.4995 ||  ||
 * 2 || 0.247 || 56 || 0.295 || 0.1651 || 0.1299 || 0.3985 || 1.5957 || 7.5677 || 0.4995 || 0.4995 || 0 ||
 * 3 || 0.247 || 56.5 || 0.295 || 0.1629 || 0.1321 || 0.4051 || 1.6088 || 7.6297 || 0.5036 || 0.5036 || 0 ||
 * 4 || 0.247 || 57.5 || 0.295 || 0.1586 || 0.1364 || 0.4183 || 1.6349 || 7.7533 || 0.5117 || 0.5117 || 0 ||
 * 5 || 0.247 || 56.5 || 0.295 || 0.1629 || 0.1321 || 0.4051 || 1.6088 || 7.6297 || 0.5036 || 0.5036 || 0 ||
 * Average || 0.247 || 56.5 || 0.295 || 0.1629 || 0.1321 || 0.4051 || 1.6088 || 7.6296 || 0.5036 || 0.5036 || 0 ||



**Calculations**
__Finding Time__ Dy = Vit + 1/2at^2 Dy=.885m, Vi = 0, a = 9.8, t =? .885 = 0 + 1/2)(9.8)t^2 t^2 = .181 t = .425 seconds

__Finding Initial Vertical Velocity (Speed when ball is shot)__
Dx = Vit Dx = 3.026m (avg), t = 0.425 seconds 3.026 = Vi(0.425) Vi = 7.12 m/s

 Finding Final Height of Pendulum cos(theta*3.14/180)=(adjacent/hypotenuse) cos(56*3.14/180)=adjacent/0.295 adjacent=0.1651m

Finding Change in Height Change in Height=Initial Height-Final Height Change in Height=0.295-0.1651 Change in Height=0.1299m

Finding Velocity of Pendulum Kei=Pef (1/2)mv^2=mgh (1/2)(0.066+0.247)v^2=(0.066+0.247)(9.8)(0.1299) v=1.5957m/s

Finding Initial Velocity of Ball in Pendulum m1v1+m2v2=m1v1'+m2v2' (0.066)v1+(0.247)(0)=(1.5957)(0.066+0.247) v1=7.5677m/s

Finding Initial Momentum of Ball p=mv p=(0.066)*(7.5677) p=0.4995 kg*m/s

Finding Final Momentum of Ball in Pendulum p=mv p=(0.066+0.247)*(1.5957) p=0.4995 kg*m/s

Finding Percent Difference Percent Difference=ABS((final-initial)/final)*100 Percent Difference=ABS((0.4995-0.4995)/0.4995)*100 Percent Difference=0%

__Conclusion__**:** Our hypothesis was definitely proven correct because our initial and final momenta for the trials were identical. This happened due to the Law of Conservation of Energy, which states that energy is maintained through a collision because it can not be created or destroyed, only transferred. This law proves why our experiment worked to perfection. Our experiment had zero error (0%). This is due to the sheer greatness of our group. More scientifically, it proves the Law of Conservation of Momentum as momentum was conserved in the system. If there was error, due to having an inferior group, this could come through air resistance. Air resistance could create a discrepancy in distance travelled. Discrepancies when the projectile is shot also should be accounted for.

The Error in our lab lab had been small, only about 8% at the most. This means that there had not been many contributing factors to error in this lab. We had concluded that this error must of come from the friction b/w the ball and the tube and the pendulum on its axis. This error could fixed with a lubrication on the friction points to reduce the friction amount to as close to zero as possible and reduce as much error as possible. We also could of used more precise measuring devices to make out info more accurate at the angles and velocity's. Real life situations this could be applied in mostly accidents that happen in the world, including car crashes, skateboarders colliding with people of objects at the bottom of ramps, and many other situations like this. If a car hits another car or a person hits another person they will usually travel together in an inelastic collision and have a momentum transfer just like in our experiment.

__Discussion Questions__: 1. In a general since when deal with collisions and momentum transfers, elastic collisions will conserve energy while inelastic collisions will not conserve energy. The most energy lost would be in an explosive inelastic collision were all of the objects energy will be lost to the explosion of the object and put into the second object. 2. A. It is inelastic because the ball travels with the ball and the final velocities are the same, and the two objects become one object. B. No because it is inelastic C. Yes, the law of conservation of momentum specifically says that in any collision momentum is conserved. 3. A. No just as stated before energy is not conserved because it is an inelastic collision. B. Yes, as said by the conservation of momentum, momentum is conserved until it reaches the maximum where velocity turns to 0 m/s. 4. A. (Ke i - Ke f ) = Ke av (1/2(.066)(7.57))-(1/2(.066)(1.60)) = Ke dif Ke dif = .2498-.0528 Ke dif = .197 J B. Ke %loss .197/.2298 21.1% C. By looking at our data alone it could be valid to say energy was conserved becuase only 21% of the energy was lost in the collision. D. M/(m+M) = .066/(.247+.066) = 21.1% The two sets of data are equl which confirms our accuracy, 5. when you increase the mass of the ball the height of the pendulum goes higher, but when you increase the mass of the pendulum its height goes up less. 6. Our velocities had not been much different having at max a %difference ofonly 8%. Most of this error came from air resistance, and friction of the ball coming out of the tube and from the pin at the top. The fix these, i would simply obtain a lubrication to reduce any and all of the friction that these are applying to the system.


 * Objective**: Find the relationship between the kinetic energy and potential energy of a pendulum


 * Hypothesis**: Due to the law of the conservation of energy, the amount of potential energy and kinetic energy should be the same since the potential energy when the bob is at the highest point should be completely converted into kinetic energy as the pendulum reaches its lowest point. Potential energy and kinetic energy should have a direct relationship.

1. String 2. Pendulum bob 3. Two photogates 4. USB port 5. Photogate port 6. Meterstick 7. Tape 8. Caliper
 * Materials**:

First, attach a piece of string to the pendulum bob. Find out the diameter of the bob by using a caliper and find the mass of the bob. Attach the other end of the string onto a table and allow the bob to hang straight down. Tape together two photogate timers and attach the photogates to a laptop. Place the two photogates directly beneath the hanging pendulum bob and tape it down. Once those are in place, measure out a height of around 0.7 meters. Pull back the bob so that the string is taut and the bob is starting from an initial position that is higher than its hanging position. The initial potential energy can be calculated by the equation Pe=mgh. Start the photogate timing and allow the bob to swing down freely and smoothly until it passes through both photogate. Collect the data that read time between gates and use that as the time. With the diameter of the bob and the time, it is now possible to find the velocity of the bob at the lowest point. The kinetic energy equation Ke=(1/2)mv^2 can be used to find the Kinetic energy of the bob. Using the same height, make 5 runs in order to obtain an average time. Run 3 trials with 5 runs each but use different heights for the other trials.
 * Procedure**:





**Sample Calculations

Actual Velocity: Diameter/Avg Time .025/.00442 5.6528 m/s

Theoretical Velocity sqrt(2aΔd) sqrt(2*10*0.714) ** 3.7789

Kinetic Energy .5*mv^2 .5*(0.014)*(5.658)^2 0.2241 J

Initial Potential Energy mgh .014*10*.752 0.1053 J

Final Potential Energy mgh .014*10*.038 .0053 J

%Error (Velocity) (Theo-Act)/Theo abs((3.778-5.658)/(3.778))*100 49.73%

%Difference (PE vs KE) (ΔPE - ΔKE)/ΔPE *100 (.1000-.2241)/(.1000)*100 124.19%

1) What role did work play in this situation? Why? Work did not play a role in this situation because the two forces present are tension force and gravitational force. Gravity does not do work on the bob and the tension force is perpendicular to the motion, therefore the tension force does not do work. The only other work is air resistance but we are neglecting it in this lab. 2) What types of energy are present when a pendulum is swinging? Potential gravitational energy and kinetic energy are present when a pendulum is swinging. 3) How do the change in PE and KE compare? Why? The change in PE and KE should always add up to a total mechanical energy. As the PE decreases, KE should increase by the same amount. This is true because there is no work being done and the law of conservation of energy states that the energy is converted from one form to another. 4) Ideally, as we've viewed it, a pendulum will swing forever. Explain why this is not actually possible, in terms of the law of conservation of energy. It is not possible for a pendulum to swing forever because there is air resistance that works against the pendulum. The air resistance, that we have neglected, will cause the bob to slow down with every passing swing. Since the law of conservation of energy states that it is impossible to have a 100% energy efficient conversion, some of the energy will be lost as heat with every transfer of energy from potential to kinetic back to potential and so on. As more and more heat is lost, the bob will eventually come to a stop. 5) What do you think would happen if you used a pendulum bob with more mass? If we used a pendulum bob with more mass, the bob will initially have more potential energy meaning that there is more conversion into kinetic energy resulting in a greater velocity. If the surface area of the bob does not change, then the amount of air resistance would be the same. However if the surface area does increase due to the increased mass, then the bob would experience more air resistance and therefore slow down more quickly.
 * Analysis/Discussion Questions**:

Conclusions

Our hypothesis was proven wrong. Kinetic energy and potential energy did not end up being the same. It ended up not being close with a 100plus percent difference. What we know instead is that kinetic and potential energy are related, but in a different way. Kinetic and Potential energy added will equal the same amount of joules at any point, assuming no energy is "lost" due to heat or the like. Increased Potential Energy would mean a decrease in potential energy, and vice versa. This makes more sense since the pendulum is fastest at the bottom of the swing, where there is the least potential energy (the height is at its lowest point). At the top parts of the swings, kinetic energy would be smaller and potential energy higher since the pendulum has 0 velocity for a brief moment, while the pendulum is at it's highest point.

In this lab, we had a significant amount of error. Since we ignored air resistance, we did not get a complete conversion of energy from potential at the initial point of the bob to the kinetic energy at the bottom. A lot of the energy was lost as heat and air resistance was also a factor that caused the incomplete transfer of energy. One possible solution to avoid this error would be to conduct the experiment in a vacuum where there is no air resistance. If no air resistance exists, then the pendulum bob might achieve a better conversion of energy from potential to kinetic. Another source of error was from the fact that we were merely eye-balling the position from where to release the bob which might have caused a different starting height for each run. This would result in a different potential energy than what we calculated. A real life application of this concept would be conducting yo-yo tricks. A professional yo-yo master might have to carefully calculate how much potential energy and at what height he or she might have to initiate the yo-yo in order to complete the trick. Sometimes the yo-yo might have to start from a higher position in order to achieve the desired velocity. The concept of the conservation of energy is important to know because most people might assume that energy is able to be destroyed and created. However, we know that energy cannot be destroyed or created, it can only be transfered from one form to another.

In this lab we obtained a substantial amount of error. For our %difference error of the Pe and Ke was 124.19%, which is obviously not a close value like we should of obtained. The Ke and Pe should be equal and many factors had added to our results. One of the major error points was air resistance on the pendulum, when doing the velocity air resistance should have been taken into account, which created some error. To eliminate an error like this we would have to either use a vacuum room so there was no air resistance, or calculate the air resistance into our calculations. Another source of error could be found in the measured height at the top and the bottom. When pulling the string up to the height, the string would sometimes pull a little bit to hard and slip slightly out of the point where it was taped to. To fix this problem, we should of found a better we to pin the rope to a certain set point. Other error problems could have been fixed by using heights not as extreme as we used, because when dropping the pendulum, the string would buckle in which would create a large amount of error and cause the pendulum to have strange variables, and an abundant amount of error. Using a material stronger then string for the swinging, to ensure it keeping straight and also keeping it at the same height, also could have fixed this. This can be seen in many real world applications such as Bulldozing, in which find out of if the energy transfer will be enough by have the ball lift up to a certain distance.

__Due: 2/11/10 Period 6__ =Work Done By Friction= Will Fassuliotis: Task A Tony Greco: Task B Tony Xu: Task C Alex McCullough: Task D

__Purpose/Objective__: To find the relationships between Initial Kinetic Energy and the amount of Work done by Friction. (B)

__Hypothesis/Rationale__: The initial Kinetic Energy and the Work done by Friction should be directly proportional, meaning as one of these values goes up the other will go up with it. This is so because theoretically the two values should equal each other. The experiment will show this by increasing the velocity meaning the Ke= 1/2mv 2 which shows as velocity raises the kinetic energy has to raise. While for work, if the velocity increase, then the distance must increase, meaning that W = Fd goes up as the distance goes up. (B)

__Procedure (Friction Force):__ 1. Using a force sensor, record data from pulling the block across the ground using 5 different weights, with 3 trials each weight 2. Create a force x mass graph using excel 3. Record the coefficient of friction from the slop of the force x mass graph 4. Solve for the force of friction by using the block and the coefficient of friction (f=mg μ**)** 5. Solve for work by using the force of friction and the distance traveled (w=fd)

1. Secure motion sensor tape to block and thread through the motion sensor 2. Lay out a tape measure in a straight line 3. "Bowl" the block down in a straight line on the ground 4. Measure the distance the box travels 5. Record a v-t graph using results from the data studio and measurements (D)

__Procedure (Kinetic Energy):__ 1. Attach photogate tape to the block that will be thrown and slide other end of tape through the photogate. 2. Bowl the block in as straight a line as possible down the hallway with the attached photogate tape. 3. Collect the data from the photogate in data studios by selecting the picket fence option under photogates and using the velocity vs. time graph. 4. Repeat step #2 five times in order to obtain five different results for 5 trials. 5. Solve for initial kinetic energy by first finding the initial velocity. 6. Use the kinematic equation (Vf^2=Vi^2+2ad) in order to find initial velocity after obtaining acceleration by selecting the mean value of the velocity vs. time graph. 7. Use kinetic energy equation to find initial kinetic energy (Ke=0.5*m*v^2). 8. Solve for percent difference between work done by friction and initial Kinetic Energy. (D)

__Data:__ (A)
 * Trial || Run || Mass (kg) || Normal Force (N) || Friction Force (N) || Average Friction Force (N) || Coefficient of Friction ||
 * 1 || 1 || 0.6809 || 6.7228 || 1.2 || 1.1667 || 0.1748 ||
 * || 2 || 0.6809 || 6.7228 || 1 ||  ||   ||
 * || 3 || 0.6809 || 6.7228 || 1.3 ||  ||   ||
 * 2 || 1 || 1.1809 || 11.5782 || 2.7 || 2.7333 || 0.2361 ||
 * || 2 || 1.1809 || 11.5782 || 2.9 ||  ||   ||
 * || 3 || 1.1809 || 11.5782 || 2.6 ||  ||   ||
 * 3 || 1 || 1.6809 || 16.4728 || 4.3 || 4.3333 || 0.2631 ||
 * || 2 || 1.6809 || 16.4728 || 4.3 ||  ||   ||
 * || 3 || 1.6809 || 16.4728 || 4.4 ||  ||   ||
 * 4 || 1 || 2.1809 || 21.3728 || 5.2 || 5.5000 || 0.2573 ||
 * || 2 || 2.1809 || 21.3728 || 5.8 ||  ||   ||
 * || 3 || 2.1809 || 21.3728 || 5.5 ||  ||   ||
 * 5 || 1 || 2.6809 || 26.2728 || 6.5 || 6.3667 || 0.2423 ||
 * || 2 || 2.6809 || 26.2728 || 6.3 ||  ||   ||
 * || 3 || 2.6809 || 26.2728 || 6.3 ||  ||   ||

__Graph:__

(C)

__Data Studio Data (Velocity vs. Time):__

(C)





__Calculations__:

Normal Force: Net Force=(mass)(acceleration) N=W N=mg N=(0.1809)(9.8) N=1.773N

Friction Force: Friction force=uN F=(0.2687)(1.773) F=0.476N

Initial Velocity: V f 2 =V i 2 +2ad

Initial Kinetic Energy: Ke=(.5)mv 2 Ke=(.5)(0.1809)(2.995 2 ) Ke=0.811 J

Work Due to Friction: W=F*d W=(0.476)(1.95) W=0.928 J

Percent Difference:

__(B)__

Magnitude of work done by friction and the kinetic energy of the block are equal to each other. **
 * Discussion Questions**
 * 1. How does the magnitude of work compare to the kinetic energy?

Work done by friction and the kinetic energy of the block are equal in magnitude and opposite in direction. Work done by friction (negative) opposes the kinetic energy (positive). **
 * 2. How do you explain the relationship between the work done and the kinetic energy?

An increase of mass would cause an increase in friction also. The coefficient of friction would not change, but the normal force would increase because of the increase in weight, which is why friction would increase. With an increase in friction would also come an increase in kinetic energy. **
 * 3. What do you think would happen if you used a block with more mass?

Work done by friction would increase if we used a rubber block because the coefficient of friction of rubber is much higher than the coefficient of friction of wood. **
 * 4. What do you think would happen if you used a rubber block instead of wooden block?

Ice would cause the friction to be much lower than the floor that we used, which would also cause the work done by friction to decrease. (D) **
 * 5. What do you think would happen if you did this experiment on ice instead of on the tile floor?

__Conclusions En Masse__ Yes, despite our 7-12% error I do believe that our hypothesis was correct. The Reason we obtained such a large percent error was from the Block both spinning and not going in a direct straight path when going forward. When looking back, if we had at least measured a direct path from the beginning directly to the block, then we could have reduced some of the error. If we also found a more consistent way of throwing the block without it spinning we could have reduced next to all of the error. This could have lengthened our distance in the Work equation; W=F*d, W=(0.476)(1.95), W=0.928 J to a smaller length and making it come closer to around our more accurate .811 J reading from the photo gate timer to obtain Kinetic Energy. Because to find Kinetic Energy, you need mass and velocity, in which mass is a constant, and the velocity comes from an electronic reading; Ke=(.5)mv2, Ke=(.5)(0.1809)(2.9952), Ke=0.811 J, is more accurate then our reading for distance. For this lab, we had a percent difference that ranged from 7.55 to 12.59 percent. These are fairly acceptable percent differences meaning that our lab was a success overall. We were able to prove our hypothesis that the initial Kinetic Energy and Work done by Friction are directly proportional. As the amount of Kinetic Energy increased, so did our work done by friction. Interestingly, our percent difference seemed to gradually decrease as our Kinetic Energy and Work done by Friction increased. The more initial Kinetic Energy there was meaning the more work done by friction, the lower the percent difference. We did however get percent difference due to a couple of reasons. According to the second law of thermodynamics, which is the law of entropy, energy in the form of heat is lost to the surroundings during the energy transfer. This means that there can never be a 100% efficient transfer of energy from one state to another. According to this law, our work done by friction would have been slightly different from the initial Kinetic Energy. Another source of error could have been the method we used to calculate the coefficient of friction. Since we used a force meter that was pulled by hand, the block with weights would not have necessarily been moving at constant velocity. The string attached to the box and the force meter might not have been precisely parallel to the floor which could also influence our coefficient of friction.  There are a few things could have caused our 12% error. First, when determining the coefficient of friction we could have not zeroed the tension meter perfectly, or could have dragged the block at a non-constant speed which would make our coefficient of friction less accurate. We could also have gotten error when we “bowled” the block down the hallway it tended to not stay in a straight line, spin a little, and even bounce on the ground slightly. This would probably be the cause for our largest chunk of error. In real life we could use this experiment for cars and their tires to ensure safety and reliability while on different surfaces.