Group+2

Lab: Rotational Kinetmatic Dan Rosen, Ian Gottheim, James Airo, Alex Barnett Period 2 Due: 4/6/10 Completed:4/5/10

For an object in circular motion, find the relationship between tangential velocity and the radius, between the angular velocity and the radius.
 * Objective**:

**Procedure:** 1. Gather materials, set up record and data studio 2. Set up data table 3. Measure distance of tab and radius 4. Find instantaneous velocity of record player using photogate by measuring time it takes for each piece of paper to go through tab 5. Use same radius and change speed of record player until every speed has been used for radius length. 6. Calculate tangential and angular velocities using equation v=wr 7. Change radius 4 more times and repeat steps 4-6 8. Graph tangential velocity vs. radius


 * Hypothesis**: As radius increases, tangential velocity increases due to their direct relationship. Also, as the radius increases, angular velocity will remain constant because the record player is still cutting out the same angle, just more area.


 * Equipment**:
 * Turntable
 * Pasco Photogates
 * Data Studio Software
 * Cardboard Disc
 * Marker
 * Ruler





Tangential Velocity=d/t Vt=.002/.014 Vt=.148 m/s
 * Sample Calculations (Trial 1)

Theoretical Velocity of Record Player in rad/s Theoretical Velocity=Set speed*2pi/60 Theoretical Velocity=78*2pi/60 Theoretical Velocity=8.164 rad/s

Experimental Velocity of Record Player (from graph) V=w*r Experimental Velocity (Angular Speed)=Vt/r Experimental Velocity=.148/.018 Experimental Velocity (Slope of graph)= 8.478 rad/s

Percent Error Percent Error=|Actual-Theoretical|/Theorectical*100 Percent Error=|8.478-8.164|/8.164*100 Percent Error=3.707%

**

**Discussion Questions

1. What happens to tangential velocity as the radius increases? Tangential velocity increases as the radius increases. This is because the record player has to travel more distance in the same time, based on the rpm. Also, tangential velocity and radius have a direct relationship.

2. ** What happens to angular velocity as the radius increases? Angular velocity remains constant as the radius increases. This is because the record player cuts out the same angle even though there is a larger radius. Only tangential velocity changes because more radius means more area covered

3. What does the slope of each line indicate? The slope of the line indicates the angular velocity. This is due to the equation v=wr. We plotted v and r, so the slope is w.

4. Why didn’t we measure the velocity by measuring the period and circumference? Finding the period and circumference for the velocity gives an average velocity. We were trying to determine the instantaneous velocity, which is why we used v=wr

5. Since we can convert everything to linear anyway, what you suppose is the point in using angular quantities? Angular quantities give a different perspective than linear quantities. It helps you picture the angle the record player cuts out as it moves a certain period of time. Linear just makes you visualize the outside of the disk moving. They are both very beneficial to understand the speed of the record player, they just show different perspectives.

Upon completion of the lab, it was evident that we satisfied the objective of the experiment and proved our hypothesis correct. As we increased the radius, tangential velocity increased as well. The angular velocity remained constant, as we predicted it would, because the record player still traveled at the same angle, despite the increasing of the radius.
 * Conclusion:

Overal, our data was very accurate. Our highest percent error was 7.965% from the 16rpm trials. One major source for this error could have came from the placement of the Photogate. The Photogate needed to be completely still to receive the most accurate data. However, it's very likely that the Photogate wasn't held completely still, which throws off our times. Those times effect the tangential velocity which then effects the angular velocity. If the times get effected by error than the angular velocity also gets effected. Also the values we used for tangential velocity are instantaneous speeds. If we timed the period of the disc and get an average tangential velocity we could have received slightly more accurate results.

The main correction that could be made to this lab is finding a more efficient way to record instantaneous velocity. The Photogate timing allowed for error due to motion of the person holding the Photogate. One real life application of this experiment would be to determine how much the size of the ferris wheel determines one's tangential velocity (because the experiment proved that the size of the radius does not affect the angular velocity). The ferris wheel with a larger radius must travel a longer distance, thus needing a greater speed in order to attain the same velocity of one with a smaller radius.

**

Lab: Ballistic Pendulum Dan Rosen, Ian Gottheim, James Airo, Alex Barnett Period 2 Due: 3/23/10 Completed:3/22/10

Objectives: - To find the initial velocity of the steel ball using projectile, work energy, and momentum - To find the relationship between initial and final momenta of a ball fired into a ballistic pendulum.

Hypothesis: The initial and final momenta of a ball fired into a ballistic pendulum will be equal due to the law of conservation of momentum. The shorter the range of the launcher, the less the initial velocity will be. Initial velocity using projectile should be equal to the initial velocity using work energy and momentum.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">__Materials__:
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Steel Ball
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Projectile Launcher
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Ballistic Pendulum
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Stand
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">String
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Carbon Paper
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Clamp
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Ruler

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">__Procedure for Projectile Method__
 * 1) <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Set up projectile launcher at a horizontal angle.
 * 2) <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Clamp the projectile launcher to the table.
 * 3) <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Set projectile to medium range when ram-rodding the ball in to the launcher.
 * 4) <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Measure the height of the launcher from the ground (along the y-axis).
 * 5) <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Place carbon paper at medium range away from projectile.
 * 6) <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Launch projectile and record the range from launcher to the ball mark made on the carbon paper.
 * 7) <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Repeat 5 times.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">__Procedure for Momentum/Energy Method__
 * 1) <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Set up projectile with ballistic pendulum
 * 2) <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Measure mass of ball and ballistic pendulum.
 * 3) <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Launch projectile into pendulum
 * 4) <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Record angle pendulum makes after being launched.
 * 5) <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Repeat 5 times.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">__Data Tables__

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<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">__Sample Calculations__

Finding Initial Velocity of Ball (Using Projectile Initial Velocity Table Trial 1)

y= - 4.9t2 -.848 m= -4.9t2 .1731= t2 .416 s = t

x= vit 1.427 m = vi (.416 s) vi= 3.43 m/s

Finding Initial Velocity of Ball (Using Momentum Initial Velocity Table Trial 1)

KEi + PEgi + PEsi + W = KEf + PEgf + PEsf KEi = PEgf (1/2) mv2 = mgh (1/2) v2 = (9.8) (L- Lcos27.8) v2= (2) (9.8) ( .3 -.3cos27.8) v2=.679 v= .823 m/s (final velocity of ballistic pendulum. This is used to find initial velocity)

v1’ = v2’ m1v1 + m2v2= (m1+ m2) v’ (.0666) v1 = (.066+.247) .823 v1= 3.87 m/s

% Difference ( Projectile Initial v. Momentum Initial)

11.4% = % difference
 * ProjectileInitial - MomentumInitial |/MomentumInitial x 100
 * 3.43-3.87| / 3.87 x 100

Momentum Percent Difference (Using Trial 1 Data)

Initial velocity of ball = 3.898 m/s Initial Momentum = mv Initial Momentum = (.0666) (3.898) Initial Momentum = .257 kg * m/s Final velocity of ballistic pendulum = .822 Final Momentum = mv Final Momentum = (.066+.247) .822 Final Momentum = .257 kg*m/s

Initial and Final Momentum are both .257 kg*m/s, so there is 0 % error.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Discussion Questions <span style="display: block; font-family: Arial,Helvetica,sans-serif; font-weight: normal; text-align: left;">Inelastic collisions do not conserve kinetic energy.In a perfect scenario, the two objects which collide will stick together thus causing the final velocities to be equal. Elastic collisions do conserve elastic energy. The velocities are equal but opposite.
 * 1.In general, what kind of collision conserves kinetic energy? What kind doesn’t? What kind results in maximum loss of kinetic energy?**

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">2.Consider the collision between the ball and pendulum. a.Is it elastic or inelastic? Elastic, because when the ball is launched and goes into the pendulum, they move together uniformly.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">**b.Is energy conserved?** Yes, due to the Law of Conservation of Energy

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">**c.Is momentum conserved?** Yes, due to the Law of Conservation of Momentum

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">3.Consider the swing and rise of the pendulum and embedded ball.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">**a. Is energy conserved from the moment just before the ball strikes the pendulum to the moment the pendulum rises to its maximum height?** Energy prior to hitting the pendulum and the energy of the pendulum at maximum height is not conserved. Since the lab exemplified an inelastic scenario, the kinetic energy is not conserved throughout.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">**b.How about momentum?** Due to the Law of Conservation of Momentum, momentum is conserved

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">**4.It would greatly simplify the calculations if kinetic energy were conserved in the collision between ball and pendulum.**

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">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.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">c.According to your calculations, would it be valid to assume that energy was conserved in that collision?

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">**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.**

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">KE before= (1/2)(m)(v^2) = (1/2)(.066)(3.436^2)= 3.896 J

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">KE after= (1/2)(m)(v^2)= (1/2)(.066)(.819^2)= .022 J

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">KE lost= 3.896- .022 =3.874 J

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Percent Lost 3.874/3.896 x 100 = 99.435 %

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">I validate the percent lost due to the fact kinetic energy is not conserved in inelastic collisions.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">**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.)** After doing the virtual aspect of the lab, I was able to conclude that increasing the mass of ball would increase the velocity, along with the height it would reach. This outcome was very predictable considering the Equation for momentum is P= mv, therefore increasing the mass and/or velocity would be directly proportional to how much of an increase or decrease the momentum would be. This,however, has the reverse affect when increasing the mass of the pendulum. When the object moving into the pendulum is lighter than the pendulum itself, the object not only has to have enough momentum to move the pendulum, but also overcome gravity which is counteractive to the objects motion on the y-axis (therefore decreasing the potential height the pendulum would reach)

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">**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?**

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;"> The chart shows that the percent difference between the two velocities in any trial is no more than 12.02 % Although this indicates a mildly high difference, when taking into account the possible error in the experiment, the results are very good. Finding the angle of the pendulum was difficult to estimate by eye, along with the true starting angle (which should have been 0). Also, the pendulum that was used had several external issues, including potential and noticeable friction on the Arm, prohibiting the pendulum from reaching its true maximum height. If I were to create a ballistic pendulum, It would have frictionless motion and would have a function in it to observe accurate angle displacements.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">__Conclusion__ After completing the experiment it was obvious that we satisfied both our objectives and hypotheses.We fulfilled the first part of our hypothesis by proving that the initial and final values for momentum are equal due to the Law of Conservation of Momentum. For this part of the experiment we received excellent data that resulted in zero percent difference for all 5 values of initial and final momentum. These excellent results can be seen in trial 1. In trial 1 we received an initial momentum value of .257 kgm/s. According to our hypothesis we should receive a final momentum value of .257 kgm/s because the initial and final momentum should be equal. As seen in trial we do receive a final momentum value of .257 kgm/s, which proves our hypothesis correct and gives us a 0% difference, and proved that momentum is conserved throughout the experiment. For the second part of the hypothesis we stated the the initial velocity of the ball should be equal using projectile and energy momentum methods. We didn't completley prove this hypothesis correct because we received a percent difference between 10-13% for each trial. We know our results were good, and would have been better with more perfect equipment. Though the results were not perfect, they definitely showed us that we would have been able to wholly prove the hypothesis, should we have had better equipment. The percent difference represents the fact that there were errors in each method, possibly more in one than in another. If we look at trial 1, we received an initial velocity value of 3.429 m/s using projectiles and 3.898 m/s using work energy and momentum, respectively. Theoretically these two values should be equivalent, but error slightly altered our values. This error lead to a 12.02% difference.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">In perfect conditions, the velocities and momenta from both the ballistic pendulum and the projectile should have been equivalent. There were many lurking variables which slightly altered these results. Our average percent difference was 11.548%. This error was the result of several imperfections in the equipment. The ballistic pendulum had several components in it which could have caused error due to friction. Also, the projectile launcher does not necessarily launch the ball with the exact same initial speed every time. Air resistance, although only a small role in determining the velocity of each, is without a doubt a factor in the error. In order to obtain better results, the ballistic pendulum could require a better tool to measure the angle displaced, along with a true angle 0, while at rest. Sometimes, we may not have noticed because we were using our eyes to determine the angel of the pendulum, but the angle may not have started at exactly 0. Overall, error was mainly a source from judging angle measures along with imperfections in equipment. For the difference between initial and final momentum, we received 0% error. This proves the Law of Conservation of Momentum to be true, that momentum is conserved through the experiment.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">The Ballistic Pendulum lab can be applied to many real life scenarios. The kinematics portion of the lab can be used to find any component of a projectile, such as the distance a basketball travels in the air or the initial velocity of a baseball as it is hit off of a bat. With the momentum portion of the lab, the applications become more interesting. Any interactions between two objects can use the law of conservation of momentum. For example, hitting a fly with a fly swatter is similar to the inelastic collision of the ballistic pendulum. The swatter comes in contact with the fly, making the fly/swatter combination have one final velocity. The momentum of both objects before the collision will equal the final momentum due to the Law of Conservation of Momentum. If a small bullet is shot at a very high velocity at a foam bored, the momentum equation can help begin to determine how far the bullet will sink in to the board, after using kinematics, and even find the velocity that the bullet would need to fully penetrate the board. This lab truly has many useful real life applications.

__Lab: Energy of a Projectile Launcher__ Dan Rosen, Ian Gottheim, James Airo, Alex Barnett Period 2 Due: 2/23/10 Completed: 2/22/10

__Objective:__ Find the relationship between the elastic potential of the compressed spring, the kinetic energy at initial projection, and the potential energy at a maximum height for a ball shot vertically upward.

__Hypothesis:__ The elastic potential, the kinetic, and the potential energies will all be equal according to the Law of Conservation of Energies and because they are the max energies at those particular points.

__Materials:__
 * Projectile Launcher and plastic ball
 * Plunger
 * Plumb bob
 * 2 photogates and photogate bracket
 * Ruler
 * Meter stick
 * Masses

__Procedure (set up)__ 1) Gather materials 2) Set up launcher, clamp to table and set up launcher vertically, perpendicular to table

__Procedure (PEs)__ 1) Tape rod to cup 2) Insert rod into cup and mark position on rod 3) Add masses of increments of .5 kg (5 times) 4) Put all data into F(spring) v. x graph

__Procedure (KEi)__ 1) Attach photogate to launcher at lowest release point 2) Launch ball 3) Repeat 5 times, record data to find vi

__Procedure (PEg)__ 1) Tape meter stick to side of launcher 2) Launch ball and record height 3) Repeat 5 times 4) Record measurements

__Kinetic Energy Maximum Chart__

__Potential Gravitational Energy Maximum Chart__

__Elastic Potential Energy Maximum Chart __






 * Sample Calculations

Kinetic Energy (using trial #1)**

d= (vo)(t) + (1/2)(a)(t^2) .0251= (vo)(.0056) +(1/2)(-9.8)(.0056^2) Vo= 4.51 m/s

KE= (1/2)(m)(v^2) KE= (1/2)(.0100)(4.5176^2) KE= .102 J


 * Potential Gravitational (using trial #1)

PEg=mgh PEg= (0.0100)(9.8)(1.0225) ** PEg= 0.100205 J


 * Potential Energy Elastic

Slope of Force Spring vs Change in Position graph titled: __Elastic Potential Energy Constant (K)__ **

Potential Elastic Max (Using the initial position of .0375m) PEs=1/2kx^2 PEs=1/2(183.57)(.0375)^2 PEs=.1286 J

It is unnecessary to calculate the work due to each of these because work due to spring is really just PEs and work due to gravity is PEg. They are both forms of potential energy, where the values can be calculated and already are representative of work. 2. How do you explain the relationship between PEs, PEg, and KE? The total energy value remains constant throughout the experiment. No energy actually leaves or enters the projectile experiment. But, the actual amount of PEs, PEg, and KE changes throughout the experiment. The three are representative of the total energy, when added together. For example, at launch, there is PEs only. While being launched, there is only KE, and while in the air there are both KE and PEg, which are equal to the total amount of energy represented in the two other points of measurement. 3. What do you think would happen if you used a ball with more mass? Each of the energy values would be greater with a more massive ball.
 * Discussion Questions: **
 * 1. Why didn’t we calculate Work due to the spring of due to gravity?

****Conclusion:**

=
After completing this lab, we have satisfied our purpose of finding the values for each type of energy and it is apparent that our original hypothesis was correct based upon how close the values were for KE, PEs, and PEg. Based upon the Law of Conservation of Energy, the three values should theoretically be equal, however each value is slightly off due to error in the experiment. Our Average KE was .1023 J, Average PEg was .1012 J and Average PEs was .1286. We received varied percent differences for each energy. Since we were dealing with such low numbers, the slightest error would greatly increase our percent differences. Because the values for each type of energy are so close the lab demonstrates how energy is merely transfered or stored, rather than gained or lost.=====

=
There are multiple ways we could have altered this lab in order to obtain more accurate results. First, finding the spring force constant served to be tricky due to the difficulty of measuring how far down the spring went (x value). Eyeballing the change in position for the spring caused error because the spring didn't move significantly when adding the weight, so it was difficult to determine the value of the constant. It was also tough to add a lot of weight because the cup holding the masses had a small bin for the masses. Our results may have been more accurate if we had a more sturdy/larger bin to add masses, because this in turn, would have made eyeballing the distance changes easier. This error led to our error in calculating PEs. Also, due to the fact we were not able to use our own launcher to calculate the spring force constant, this part of the experiment yielded significant error. When comparing Peg and PEs, there was a 27.1 % difference, KE and PEs had a 25.7 % difference and KE and PEg only had a 1.08% difference, proving how statistically significant and faulty our calculating of PEs was. Another way to improve the experiment would be to use a motion detector as opposed to eye balling the distance and measuring with a meter stick. This would have gave us more accurate results and in turn, given us a more accurate constant value. Although we had four pairs of eyes watching, no one could accurately approximate when eyeballing. Although we received a large error, it was common flaw seen in other groups' experiment.=====

This experiment holds relevance to many facets of life; even something as simple the "T-Shirt Launch" at various basketball games and other sporting events. Mascots and other representatives of the home team during a timeout or halftime show launch T-shirts promoting their team and/or sponsor of the team. Each launcher is identical, but the person who launched the t-shirts is able to vary the distance at which the shirt is launched by adjusting the severity of the compression of the spring. The more compressed the spring on the launcher is, the further the shirt will fly. Each person launching the t-shirts should be aware of how fast (KE) the launcher sends each shirt (PEs). By doing so, each person can attempt to target a specific fan or section.

Lab: Work Done by Friction Dan Rosen, Ian Gottheim, James Airo, Alex Barnett Period 2 Due: 2/9/10 Completed: 2/8/10

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

__Hypothesis__: The initial kinetic energy and the amount of work done by friction will be directly proportional. This is because the more energy in the equation, the more work friction will need to do in order to counteract the energy.

__Materials:__ -piece of wood -10 meter tape measure -string -force sensor -data studio -motion sensor -scale

__Procedure (Friction Force)__ 1. attach force sensor to block and pull on ground at constant speed 2. do multiple (5) trials in data studio to measure kinetic friction 3. Create a graph of the trials and calculate the slope to find the coefficient of kinetic friction 4. find normal force of block, and multiply normal force of block on ground with the friction coefficient to find friction force (f=uN) 5. designate a starting point 6. use work equation to find value of work using distance and force (W=d*F)

__Procedure (Kinetic Energy)__ 1. connect wood to motion sensor 2. throw block, observe time and acceleration from data studio. Also Record the Distance. Repeat 5 times 3. plug distance, acceleration, time, to find initial velocity 4. plug in initial velocity and mass into KE=1/2(m)(v)^2

__Coefficient of Friction Table__ __Kinetic Energy Table__
 * Trial || Mass (kg) || Force of Kinetic Friction (N) || Normal Force (N) || Average Friction (N) || Friction Force Using Coefficient of Friction (N) (using slope of graph, .202) || Work Done by Friction (Joules) ||
 * 1a || 0.195 || 0.2 || 1.911 || 0.3 || 0.386 || -1.081 ||
 * 1b ||^  || 0.4 ||^   ||^   ||^   ||^   ||
 * 1c ||^  || 0.3 ||^   ||^   ||^   ||^   ||
 * 2a || 0.695 || 1.2 || 6.811 || 1.3 || 1.376 || -3.605 ||
 * 2b ||^  || 1.3 ||^   ||^   ||^   ||^   ||
 * 2c ||^  || 1.4 ||^   ||^   ||^   ||^   ||
 * 3a || 1.195 || 2.2 || 11.711 || 2.3 || 2.366 || -6.955 ||
 * 3b ||^  || 2.5 ||^   ||^   ||^   ||^   ||
 * 3c ||^  || 2.3 ||^   ||^   ||^   ||^   ||
 * 4a || 1.695 || 3.2 || 16.611 || 3.3 || 3.355 || -9.932 ||
 * 4b ||^  || 3.3 ||^   ||^   ||^   ||^   ||
 * 4c ||^  || 3.3 ||^   ||^   ||^   ||^   ||
 * 5a || 2.195 || 4.1 || 21.511 || 4.3 || 4.345 || -12.210 ||
 * 5b ||^  || 4.3 ||^   ||^   ||^   ||^   ||
 * 5c ||^  || 4.4 ||^   ||^   ||^   ||^   ||
 * Trial || Distance(m) || Final Velocity (m/s) || Acceleration(m/s/s) || Initial Velocity(m/s) || Mass (g) || Initial Kinetic Energy (J) || Percent Difference of Initial Kinetic Energy vs. Work Done By Friction (%) ||
 * 1 || 2.80 || 0 || -1.93 || 3.288 || 0.195 || 1.054 || 2.03 ||
 * 2 || 2.62 ||^  || -1.43 || 2.737 || 0.695 || 2.604 || 2.38 ||
 * 3 || 2.94 ||^  || -2.73 || 4.007 || 1.195 || 9.591 || 1.73 ||
 * 4 || 2.96 ||^  || -2.74 || 4.028 || 1.695 || 13.747 || 1.72 ||
 * 5 || 2.81 ||^  || -1.93 || 3.293 || 2.195 || 11.904 || 2.03 ||

Sample Calculation (Using Trial 1)

> <span style="font-family: sans-serif,helvetica,sans-serif;">(There exists a negative number for the work done by friction because friction is opposing motion.)
 * __To find Frictional Force__
 * <span style="font-family: sans-serif,helvetica,sans-serif;">Friction= (Coefficient of Friction)(Normal Force) Normal Force= (Mass)(Gravity)
 * <span style="font-family: sans-serif,helvetica,sans-serif;">Friction= (0.202)(.195 kg x 9.8 m/s^2)
 * <span style="font-family: sans-serif,helvetica,sans-serif;">Friction= .386 N
 * <span style="font-family: sans-serif,helvetica,sans-serif;">__To find Work done by Friction__
 * <span style="font-family: sans-serif,helvetica,sans-serif;">Work= (Force)(Distance)Cos θ
 * <span style="font-family: sans-serif,helvetica,sans-serif;">Work=(.386 N)(2.8 m)Cos180
 * <span style="font-family: sans-serif,helvetica,sans-serif;">Work= -1.081 J
 * <span style="font-family: sans-serif,helvetica,sans-serif;">__To find Kinetic Energy__
 * Vf^2=Vo^2+2a<span style="font-family: Arial,Helvetica,sans-serif;"> Δd
 * 0=Vo^2+2(1.93)(2.80)
 * <span style="font-family: Arial,Helvetica,sans-serif; line-height: 16px;">Initial Velocity= 3.288 m/s
 * <span style="font-family: Arial,Helvetica,sans-serif; line-height: 16px;">KE=1/2(m)(v^2)
 * <span style="font-family: Arial,Helvetica,sans-serif; line-height: 16px;">KE=(1/2)(.195 kg)(3.288^2)
 * <span style="font-family: Arial,Helvetica,sans-serif; line-height: 16px;">KE=1.054 J
 * <span style="font-family: Arial,Helvetica,sans-serif; line-height: 16px;">__To find Percent Difference__

__Graphs Data Studio V vs T graph to find acceleration__

__Coefficient of Friction Graph__

__Discussion Questions__ 1 . How does the magnitude of work compare to the kinetic energy? The magnitude of work done by friction is equal to the magnitude of the initial kinetic energy of the block of wood.

2. How do you explain the relationship between the work done and the kinetic energy? The work done by friction and the kinetic energy of the wood block are equal but opposite. The work done by friction is negative because it is opposing the block's motion, while the initial kinetic energy is positive.

3. What do you think would happen if you used a block with more mass? If we used a block with more mass, the friction would be increased. This is because friction is equivalent to the normal force on the block times the coefficient of friction. The coefficient would remain the same, but the normal force would increase with more mass, thus increasing the friction force. Since the friction force would increase, the magnitude of the work done by friction would increase. Also, since the mass would be increased, the initial kinetic energy would increase.

4. What do you think would happen if you used a rubber block instead of wooden block? The coefficient of friction of wood is significantly lower than that of rubber. A rubber block would increase the work done by friction on the block, causing the block to have a smaller displacement than by using a wooden block.

5. What do you think would happen if you did this experiment on ice instead of on the tile floor? The block on ice would have a smaller value of friction than on the surface we used. This would cause the work done by friction to decrease drastically, while the displacement of the block on the ice would increase.

__Conclusion__

Upon completion of the lab, we realized that we had satisfied the purpose of the experiment, because we were able to find the relationship between work done by friction and kinetic energy. We however realized that our hypothesis was incorrect because there was not a direct correlation between the two. There actually existed an inverse relationship.

In conclusion, we received an average Kinetic Energy of 7.78 J and an average Work due to friction of 6.77 J. The percent difference ranged from 1.72% -2.38%, proving the overall success of the lab and the magnitude of both are equal. The greatest source of error was caused by the uneven surface where the experiment was conducted. The data was collected from bowling the block in a garage, which has many lurking variables which could alter the results. The garage floor was dusty and someone inconsistent. Though it was relatively smooth throughout, certain bumps and imperfections may have caused our results to be slightly flawed. Despite all of the potential problems the surface could have caused, the marginal error demonstrates the success of the experiment. Another source of error comes from the combination of theoretical and experimental values. A majority of the calculations were based off of experimented data which is where most of the error lies (human error). Overall the experiment was of great success, yielding no more than a 2.38% difference.

The lab could use some variations to help any error that occurred. When finding the coefficient of friction, it might have been more accurate to go online and find the true coefficient. This is because our experimental findings had several cases of human error, such as not pulling the block directly parallel to the ground. By using the true value, it could have given our group a more accurate friction force, thus giving us a more accurate value for the work of friction. Also, to defray from receiving any error from bowling the wooden block, a better approach would be to use a machine or a device that could push the block across the floor. By throwing the block, there could have been some minor bouncing that would affect our velocity, which would make our coefficient of friction not make sense.

This lab has great relevance to everyday life. Tire companies should use the concepts in this lab. It would be beneficial to know the work done by friction at different initial kinetic energies because the tire companies can create the safest tire possible. A tire with a greater coefficient of friction could make it possible to stop at higher kinetic energies than a tire with a smaller coefficient of friction on concrete. The relationship between initial kinetic energy and the work done by friction is valuable making this lab very beneficial and informative.