Group+7

Due: 4/8/10
Objective:  For an object in circular motion, what is the relationship between tangential velocity and the radius? Between the angular velocity and the radius?
 * Hypothesis:**

=
As the radius increases the angular velocity remains constant. As the radius increases the liner velocity increases. This is because to get from angular velocity to tangental velocity you multiply the angular velocity by the radius.======

Plug in the turntable and place the cardboard disk on top. Assemble the Photogate sensor and open Data Studio (Photogate Timer). Place Velcro marker on the Velcro strip on the cardboard disk and measure its distance from the center using a ruler (m). Run the turntable so it spins at 75rpm. Allow it to run several seconds. Hold the Photogate over the Velcro so that Data Studio records the time it takes the marker to pass through the gates. Do 3 trials at this speed and radius, then repeat for 5 different radii, further repeating the entire process for each speed setting. Record data in a table and calculate the velocity of the marker (using its width in m as the value for distance). Create a graph to prove hypothesis.
 * Procedure:**


 * Materials:** Turntable, Pasco Photogates and Data Studio, cardboard disk and marker, ruler.

Based off of Trial #1 in 78 RPM
 * Sample calculations:**

Tangental velocity: (Width of tab)/(Average Time in Photogate) (.02m)/(.095s)=.210m/s

Theoretical angular velocity: (2)(RPM)(3.14/60) (2)(75)(3.14/60)= 8.164 rad/s

% difference [(theoretical-actual)/theoretical]*100 [( 8.164-7.900)/8.164]*100= 3.23% (m/s) ||
 * Data:**
 * Data for 78 rpm ||
 * Trial || Width of Tab (m) || Length of Radius (m) |||||| Time in Photogate || Average Time (s) || Velocity
 * ^  ||^   ||^   || 1 || 2 || 3 ||^   ||^   ||
 * 1 || 0.02 || 0.02 || 0.093 || 0.097 || 0.096 || 0.095 || 0.210 ||
 * 2 || 0.02 || 0.04 || 0.061 || 0.063 || 0.061 || 0.062 || 0.324 ||
 * 3 || 0.02 || 0.06 || 0.043 || 0.044 || 0.043 || 0.043 || 0.462 ||
 * 4 || 0.02 || 0.08 || 0.032 || 0.033 || 0.031 || 0.032 || 0.625 ||
 * 5 || 0.02 || 0.10 || 0.027 || 0.025 || 0.024 || 0.025 || 0.789 ||

(m/s) ||
 * Data for 45 rpm ||
 * Trial || Width of Tab (m) || Length of Radius (m) |||||| Time in Photogate || Average Time (s) || Velocity
 * ^  ||^   ||^   || 1 || 2 || 3 ||^   ||^   ||
 * 1 || 0.02 || 0.02 || 0.152 || 0.148 || 0.149 || 0.150 || 0.134 ||
 * 2 || 0.02 || 0.04 || 0.097 || 0.096 || 0.097 || 0.097 || 0.207 ||
 * 3 || 0.02 || 0.06 || 0.067 || 0.064 || 0.063 || 0.065 || 0.309 ||
 * 4 || 0.02 || 0.08 || 0.051 || 0.049 || 0.052 || 0.051 || 0.395 ||
 * 5 || 0.02 || 0.10 || 0.043 || 0.039 || 0.044 || 0.042 || 0.476 ||

(m/s) ||
 * Data for 33 rpm ||
 * Trial || Width of Tab (m) || Length of Radius (m) |||||| Time in Photogate || Average Time (s) || Velocity
 * ^  ||^   ||^   || 1 || 2 || 3 ||^   ||^   ||
 * 1 || 0.02 || 0.02 || 0.210 || 0.213 || 0.21 || 0.211 || 0.095 ||
 * 2 || 0.02 || 0.04 || 0.121 || 0.118 || 0.119 || 0.119333333 || 0.168 ||
 * 3 || 0.02 || 0.06 || 0.088 || 0.086 || 0.084 || 0.086 || 0.233 ||
 * 4 || 0.02 || 0.08 || 0.067 || 0.066 || 0.063 || 0.065 || 0.306 ||
 * 5 || 0.02 || 0.10 || 0.053 || 0.059 || 0.059 || 0.057 || 0.351 ||

(m/s) ||
 * Data for 16 rpm ||
 * Trial || Width of Tab (m) || Length of Radius (m) |||||| Time in Photogate || Average Time (s) || Velocity
 * ^  ||^   ||^   || 1 || 2 || 3 ||^   ||^   ||
 * 1 || 0.02 || 0.02 || 0.419 || 0.416 || 0.414 || 0.416 || 0.048 ||
 * 2 || 0.02 || 0.04 || 0.241 || 0.243 || 0.241 || 0.242 || 0.083 ||
 * 3 || 0.02 || 0.06 || 0.171 || 0.173 || 0.170 || 0.171 || 0.117 ||
 * 4 || 0.02 || 0.08 || 0.142 || 0.142 || 0.141 || 0.142 || 0.141 ||
 * 5 || 0.02 || 0.10 || 0.113 || 0.117 || 0.111 || 0.114 || 0.176 ||


 * RPM || Theoretical Angular V (rad/s) || Experimental Velocity (rad/s) || Percent Difference % ||
 * 78 || 8.164 || 7.900 || 3.23% ||
 * 45 || 4.710 || 4.941 || 4.90% ||
 * 33 || 3.454 || 3.734 || 8.11% ||
 * 16 || 1.675 || 1.826 || 9.04% ||



1. What happens to tangential velocity as the radius increases? As the radius increases, the tangential velocity also increases. This is because the further the radius moves toward the circumference of the circle, the more distance it has to cover in the same amount of time. Therefore, the tangential velocity is faster. Tangential velocity also depends on the length of the radius. 2. What happens to angular velocity as the radius increases? As the radius increases, the angular velocity remains constant. This is because the angle on the circle remains the same as the radius moves further out. Also, the angular velocity does not depend on the length of the radius. 3. What does the slope of each line indicate? The slope of each line indicates the experimental angular velocity of each speed value. 4. Why didn’t we measure the velocity by measuring the period and circumference? This would only yield an average velocity, whereas using the angular velocity equation gives an instantaneous velocity which is more precise. 5. Since we can convert everything to linear anyway, what you suppose is the point in using angular quantities? Angular quantities pertain to objects moving in a circle, whereas linear quantities do not. Therefore angular quantities are appropriate for this scenario.
 * Analysis:**


 * Conclusion part 1**- In this lab we were supposed to find the relationship between tangential velocity/ angular velocity and the radius. This objective was met, and our hypothesis was correct. The radius does not affect the angular speed, yet it increases the tangential speed speed also increases. This is proven when the disk is at 16 rpm and the speed when the radius is .02m and the speed is .048m/s. When the radius increases to .10m, the velocity increases to .176m/s. Through all of these the angular velocity remained constant unless the rpm of the disk was changed.


 * Conclusion part 2**- In this lab the error was not horrible.


 * Conclusion part 3-** To reduce the amount of error in the lab, we could have found a way to stabilize the Photogate timer. By holding it over the turntable, the time it took for the marker to pass through may have faltered from trial to trial. The concept of rotational kinematics applies to, for example, a spinning amusement park ride. If you sit at the edge of the spinning circle, you will feel like you're moving faster because your tangential velocity will be greater than if you were sitting closer to the center. However, your angular velocity will not change.

Lab #18- Ballistic Pendulum By: Danny Schneider, Robbie Klecanda, and Alanna Smith Period 6: Completed on: March 18th, 2010 Due: March 25th, 2010


 * Objective**: 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. This is a result of the Law of Conservation of Momentum in which the momentum of a system remains constant, and thus the initial and final momenta of the ball fired into a ballistic pendulum will be equal. Similarly, the initial velocity of the ball found using the projectile method should be the equal to the velocity that was found using the energy/momentum method.


 * Materials:** Projectile Launcher and steel ball, plumb bob, meter stick, C-clamp, mass balance 




 * Procedure:** Before beginning, mass the steel ball using the mass balance. Then, tape a piece of computer paper on top of a piece of carbon paper, and tape both papers on the ground some distance in front of the projectile launcher (with the computer paper side facing the floor). Assemble the Projectile Launcher and place on a flat surface. First set the launcher to "long range" and pull the string to launch the steel ball. See if the ball hits the paper on the ground. If not, adjust the paper and launcher so that the ball hits the paper every trial. Once this is established, launch the ball five times, lifting the carbon paper up to label the mark for each trial. Then, measure the distance from the edge of the launcher to each mark on the computer paper, using a meter stick as a measuring tool. Record results for later.

Next, hang the C-clamp from the top of the launcher so that when you pull the string, the ball shoots directly into the C-clamp. Pull the string to launch the ball five times into the clamp and observe the angle at which the clamp reaches its maximum height. Record this angle value in degrees for each trial, and compute an average angle. Also, measure the length of the clamp itself (from the top of the launcher to the middle of the launcher mouth) and record for later.

Finally, employ both Work-Energy and momentum concepts, along with the given and measured information, to calculate the initial and final momentums of the pendulum.


 * Data:**




 * Calculations**:
 * Discussion Questions:**

1. In general, what kind of collision conserves kinetic energy? What kind doesn’t? What kind results in maximum loss of kinetic energy?- In general, an elastic collision conserves kinetic energy and an inelastic collision does not. However, an explosive inelastic collision results in maximum loss of kinetic energy.

2. Consider the collision between the ball and pendulum. 1. Is it elastic or inelastic?- The collision is inelastic. 2. Is energy conserved?- Kinetic energy is not conserved. 3. Is momentum conserved?- Since Kinetic energy is not conserved, momentum is also not conserved.

3. Consider the swing and rise of the pendulum and embedded ball. 1. Is energy conserved from the moment just before the ball strikes the pendulum to the moment the pendulum rises to its maximum height? Kinetic energy is not conserved because the final velocity is 0m/s. 2. How about momentum? Momentum is also not conserved because the pendulum stops moving.

4. It would greatly simplify the calculations if kinetic energy were conserved in the collision between ball and pendulum. 1. Calculate the loss in kinetic energy as the difference between the kinetic energy before and immediately after the collision between ball and pendulum. (4.952-4.909) = .043 J of KE 2. What is the percentage loss in kinetic energy? Find by dividing the loss by the original kinetic energy. (4.952-4.909)/(4.952) = .86 % loss 3. According to your calculations, would it be valid to assume that energy was conserved in that collision? Yes, since the calculations show that there is only a .86% loss of Kinetic energy, it is safe to assume this loss is negligible and kinetic energy was conserved in the collision.

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.)

Increasing the mass of the ball yields a higher maximum height of the pendulum. Increasing the pendulum mass decreases the maximum height of the pendulum

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?

No, there are not significant differences between the initial velocity of the ball and the initial velocity of the pendulum. A heavier ball mass may increase this difference, or perhaps a lighter pendulum mass. To have the momentum method yield better results, the hanging length should be shorter so the distance is decreased, with less chance for error.

**Conclusion/Evaluation (Parts 1,2,3):** Through the experiment using a ballistic pendulum, the purpose most certainly was satisfied. The purpose was to determine the relationship between initial and final momenta of a ball fired into a ballistic pendulum, originally expressing their equality in our hypothesis. Separately, we hypothesized that the initial velocity should be equal using projectile and energy/momentum methods. Through our experiment and data, we satisfied these ideas. First, we confirmed the equality of the initial and final momenta. For example, in Trial One and the methods shown in calculations above, we determined the momentum of the ball to be 0.32504 Ns. Meanwhile, the momentum of the ball and the pendulum, which was not with the ball and pendulum as one (now had a higher mass because the mass of the pendulum is taken into account but the velocity of p=mv is no different, although the final velocities in the LCM equation are equal because the ball and pendulum are sticking as one), was also 0.32504, the exact same momentum before and after the collision. This gave a 0% error for Trial One. Amazingly enough, Trial One, Two, Three, Four, and Five all had a 0% error, representing the exact momenta before and after the collision. This data strongly suggests the accuracy of the Law of Conservation of Momentum and how momentum was fully conserved during the collision. Separately, we hypothesized that the initial velocities found through the projectile and the momentum/energy methods portrayed in calculations would be the same. The data was fairly consistent, giving a range of percent differences between the two sets of data from 0.50% in trial 5 to 4.24% in trial 4. This consistent data with fairly low percent differences also suggests the similarity between the two initial velocities, nearly confirming one’s ability, as our hypothesis stated, to determine the initial velocities by both projectile and energy/momentum methods. Overall, this data satisfied our purpose as we determined the relationship between initial and final momenta of a ball fired into a ballistic pendulum, additionally exemplifying our hypothesis as correct considering the two were equal. Regarding the initial and final momenta, there was absolutely no error that occurred. The percent differences throughout the five trials were all zero percent, demonstrating the equality of the two momenta before and after the collision. This served to prove the Law of Conservation of Momentum, showing how momentum was conserved during the collision. As for the velocities through the two methods, projectile and momentum, there were errors. The errors were relatively small, but errors nonetheless, ranging from 0.50% in trial 5 to 4.24% in trial 4. While still demonstrating one’s ability to find initial velocities (and showing their equal) through the two methods, this error in the differing velocities could have occurred from several sources, most likely while performing the momentum sector of the experiment. First, the needle against the ballistic pendulum may have prevented the ballistic pendulum from reaching fully possible movement. So, there may have been this force between the ballistic pendulum and the surface. While performing the projectile method, air resistance may have accounted for the slight error by varying the distance the ball traveled. Finally, the measurements of the height of the pendulum itself may have been a bit skewed considering it was eyed and not scientifically calculated with aid of a electronic device, possibly allowing for some error. The first of these sources could have been alleviated by using a sort of computer laser system, possibly attached the ballistic pendulum which measured the maximum angle it reached without actually touching a surface. Air resistance could be minimized by removing the strong air flow of the room, or even made a little bit smaller by turning off the fan located by our experiment in the corner of the room where the experiment was performed. The third error could have been alleviated with a more exact measurement in which a straight beam of light/laser measured the exact point from the middle of the projectile launcher to the exact measurement on the ruler, where we could then use this value as our height. These various errors may have accounted for the slight errors between the initial velocities found by projectile and energy/momentum methods. At the same time, it still showed our hypothesis to be correct because the data was consistent in demonstrating the similar values of the two initial velocities. This lab is essentially a multidisciplinary physics problem, incorporating many aspects of physics concepts. As we continue to study, I’m sure we will come across more methods of solving for the same variables in real-life problems, thus furthering our understanding of the world and how it works. We can apply the concepts to actual pendulums such as musical metronomes and construction wrecking balls. Using these concepts, we can calculate velocities, heights, accelerations, etc. of these particular situations which may be useful, given the circumstance. To decrease error in this lab, we could have used a more precise measuring device to measure distance, such as incorporating strings, tape measures, and plumb bobs. Also, we could have run more trials to further compare and contrast the data with our conclusions.



Lab #17- Energy of a Pendulum By: Danny Schneider, Robbie Klecanda, and Alanna Smith Period: 6 Completed on: February 11th, 2010 Due: February 25th, 2010


 * Objective**: To determine the relationship between the kinetic energy and potential energy of a pendulum.


 * Hypothesis:** Potential energy is based on PE= m*g*h, and as height increases, so should the velocity, thus increasing the kinetic energy which is based on the equation KE=0.5mv^2. The experiment should demonstrate that as height and velocity increase together, the amount of potential and kinetic energy involved in the movement of the pendulum increases as well, creating a direct relationship between the two. However, when the pendulum is held at a certain height before being released, it has gravitational potential energy (because PE= mgh, and there is height) but the kinetic energy is zero (because KE = 1/2*m*v^2 and the velocity is zero) and when the ball reaches the bottom, there is kinetic energy as the ball now has velocity, but no height and thus no gravitational potential energy.

Tie a string to the hook on the cylinder and tape the string to the edge of a flat surface so the cylinder hangs toward the floor, creating a pendulum. Measure the distance between the bottom of the cylinder at its lowest point and the floor (L) in meters using a meter stick. Tape two Photogate timers together and again to the floor in a position so that when the pendulum is released from a given height t swings through both Photogate time sensors. Measure the diameter of the cylinder in meters (D) using a caliper. Attach the photogates to Data Studio using a USB port. Select "time between gates" on the Data Studio list. Press start on Data Studio and release the pendulum from a given height (h) from L. Measure h using a meter stick in meters. Only allow the pendulum to pass through the gates once. Do 3 trials at this h value and record the time in seconds for each trial, denoted by Data Studio. Repeat this process for 5 different h values. Then, divide D/t for each h value, where t is an average of the time values at that h value. This will find the velocity of the pendulum at its lowest point. Use an average of the five velocity values calculated to find kinetic energy of the pendulum in Joules, using the formula for kinetic energy. Mass the cylinder in kilograms, then use this value and the value for L to calculate potential energy of the pendulum in Joules, using the formula for potential energy (assume the floor is ZERO). Compare the values for potential and kinetic energies for the pendulum and analyze this with the hypothesis.
 * Procedure:**


 * Materials:** String, pendulum bob, 2 photogate timers, USB port, photogate port, meter stick, caliper, Data Studio, tape


 * Setup:**




 * Data:**




 * Calculations**:







1. What role did work play in this situation? Why? Work plays no role in this experiment. While there are in fact two forces acting on the pendulum bob, force of gravity and force of tension, gravity does not do external work and the force of tension acts perpendicular to the motion of the bob. Therefore, no work is being done in this scenario. 2. What types of energy are present when a pendulum is swinging? Both potential energy and kinetic energy are present when the pendulum is swinging. 3. How do the changes in PE and KE compare? Why? The values for PE and KE always add up to a constant mechanical energy value. This is only true because there is no work acting on the pendulum bob. 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. In reality, a pendulum cannot swing forever because air resistance acts against the bob. In a vacuum, the pendulum would in fact swing forever. However, when air resistance exists, it acts as a force doing work against the system. Thus, because energy cannot be destroyed, some energy is dissipated as heat and the bob does not retain the same energy it needs to maintain its swing. 5. What do you think would happen if you used a pendulum bob with more mass? A more massive pendulum bob would move through the air more quickly, therefore preventing air molecules from moving out of the way of the system fast enough. So, this bob would encounter more air resistance and slow more quickly.
 * Analysis:**

Through the experiment performed, the purpose was satisfied. The purpose and objective of the laboratory was to find the relationship between the kinetic energy and potential energy of a pendulum, one in which our hypothesis predicted to be a direct relationship. The experiment did exemplify that the kinetic energy and potential energy shared a direct relationship in which when one increased, so did the other. This is because potential energy is partially based on height the ball starts at in the pendulum because potential energy is based on the equation PE= m*g*h, where “h” equals height. Thus, as height increases so did the potential energy. In addition, as the height increased so did the velocity because the ball, accelerating due to gravity, was accelerating for a longer period of time at the higher height. For example, in trial one of the lab the ball began at a height of 0.74 meters, and the average velocity was 3.6630 meters/second. As the height was raised to 0.84 meters, the average velocity increased to 3.8071 meters/second, portraying how with height increasing the velocity increased, as well. As velocity increases, so does kinetic energy which is based on the equation KE=0.5mv^2, so as “v” increases, so does kinetic energy. Therefore, with as height increases, so do both the potential and kinetic energy -a direct relationship. This was justified and supported by the experiment. For example, in Trial 1, the initial potential energy was calculated to be 0.1740 Joules. In trial 2, in which the height was raised by a margin of 0.1 meters, the potential energy raised to 0.1976 Joules, a distinct raise with an increase in height. Similarly, kinetic energy was calculated to be 0.1610 in trial 1, and raised to 0.1739 in trial 2. Similar and even more marginal increases occurred in the other 4 trials. Therefore, potential energy and kinetic energy have a direct relationship in which they both increased as height increased and were very similar, demonstrating that the hypothesis is correct. Furthermore, when the pendulum was held at a certain height before being released, it had gravitational potential energy which measured to be approximately 0.1740 Joules at the height of 0.74 meters (because PE= mgh, and there is height) but the kinetic energy is zero (because KE = 1/2*m*v^2 and the velocity is zero). When the ball reached the bottom, there was kinetic energy as the ball now had velocity, but a small height off the ground resulted in a relatively low gravitational potential energy, and the sum of the kinetic and potential energy would remain constant throughout the energy transfer. The experiment and its results, overall, supported the hypothesis and showed it to be correct. However, while the experiment did prove to be a success and supported the hypothesis exploring the direct and similar relationship between potential and kinetic energy, there were some errors that occurred. We found the theoretical velocity using KE = (1/2)*(m)*(v^2) with numbers from the potential energy in which KE = PEinitial – PEfinal (because there was potential energy at the bottom where the ball was slightly higher than the floor and its photogates), had a 1.53% error from the experimental velocity. This was a small percent error which signified the consistency and accuracy of the experiment conducted. There was also a small percent difference of 3.01% between the potential and kinetic energies, also signifying little error and consistency in the 5 trials. This also helped to prove our hypothesis, showing the similarity between the potential and kinetic energy and their direct relationship in which as the height increased, so did the velocity, thus increasing both the kinetic energy and potential energy. The error occurring in the experimental velocity and difference between the kinetic and potential energies was due to various sources of error. The most likely and largest source of error was the fact that our distances, both that between the ball and floor at the end position when it was straight down, and the five distances at which the ball was released, were eyed and in no way exact. This would have skewed the heights, throwing off the potential energy calculated based on the equation (Potential Energy = mass * 9.8 * height) and separating the experimental values found by the photogates to determine kinetic energy and that found theoretically with the above equation to find potential energy. There also could have been air resistance not allowing the small and light ball to fully be accelerated. This would have skewed results because the ball would not have reached capabilities regarding the velocity. In addition, although not a huge source of error, the distance of the ball diameter, a very small object, may not have been perfectly determined considering it, too, was eyed and not thoroughly examined, which would have changed the average velocities in m/s of the ball. The ball’s mass of .024 kilograms (24 grams) may also have been slightly off considering the scale used does not show exact decimal digits. These are various possible reasons why the aforementioned errors may have occurred. In order to address these errors we could have done a few things differently. Ideally, we’d like to perform this experiment in a vacuum, where no air resistance exists and we could physically and continually see the law of conservation of energy at work. This way, we could also attain more data points over a period of time and procure a more exact velocity value. As for certain things to alleviate sources of error, we could have also used an electronic device to measure the height of the pendulum, as opposed to a meter stick, for more exact height values. Pendulums exist all over. The most common example is inside a grandfather clock. But they also exist in musical metronomes, construction wrecking balls, hypnosis techniques, and even playground swings. But on a deeper level, conserving energy is an important concept to understand as it applies to not only mechanical energy, but all kinds of energy. By understanding that energy is a conservation process and is only “lost” or dissipated when another force acts upon it can help us conserve energy in the home and waste less than we consume.
 * Conclusion/Evaluation (Parts 1,2,3):**

Lab #16 - Work Done By Friction By: Danny Schneider, Robbie Klecanda, and Alanna Smith Period: 6 Completed on: February 4th, 2010 Due: February 11th, 2010


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

****Hypothesis/Rationale****:** By determining the coefficient of kinetic friction between the block and the hallway floor, the weight of the block, the initial velocity of the block by using DataStudio and a photogate, and the distance the block travels for each throw, we will find the initial kinetic energy and word done by friction. These two values, the initial kinetic energy and the amount of work done by work, will be equal, and thus directly proportional. In other words, the more kinetic energy, the more work done by friction present. As you throw the block faster, by the equation KE = mv^2, the greater initial velocity will result in a higher kinetic energy. Also with a faster throw the distance the block travels will increase and thus is subject to more work by friction by the equation W= F * d * cosθ where d (representing distance) has now increased. Both the initial kinetic energy and work done by the friction between the block and the ground will increase and be equal, a directly proportional relationship.

To find the coefficient of friction between the wooden block and the floor, attach the force sensor to the bock by a string. Add free masses to the block. Pull the sensor toward you at a constant speed. Since at constant speed acceleration = 0 m/s/s, Friction Force = Tension Force (N). Attach the sensor to Data Studio before pulling to find the force of friction (N) vs. time (s). Using the graph made in Data Studio, determine the force of kinetic friction. Record results and repeat for five free mass values. Plot all values on a Friction vs. Normal Force graph (N). The slope of this graph is the coefficient of kinetic friction. Mass the block (without any free masses attached) on the balance in kg. Use this value to calculate the work done by friction, using the equation Work = fdcos(phi). Tape the photogate timer to the floor and attach it to Data Studio. In Data Studio, choose the picket-fence option for photogate timer. Tape a piece of picket-fence tape to the block and thread it through the photogate. Bowl the block on the floor 5 times, measuring the distance the block travels with a measuring tape for each trial. In Data Studio, select a velocity (m/s) vs. time (s) graph. Extract the slope of the velocity value at t = 0s for each trial. This value is the acceleration m/s/s at t=0s. Use this value in a kinematics equation to find initial velocity. Use the velocity value and the mass of the block to calculate kinetic energy = 1/2mvsquared. Compare this value with the Force of work done by friction. Do a %error calculation.
 * Procedure:** (Alanna)


 * Materials:** 10 m tape measure, block of wood, force sensor, Data Studio, motion sensor, string, scale, photogate timers, picket-fence tape.

We used the slope from the velocity functions on this graph to find the acceleration for each trial.
 * Raw Data** (Robbie)


 * Data Tables** (Robbie)
 * Graph: Coefficient of Friction** (Robbie)





__Sample Calculations__: (Based on Trial #1) (Robbie)


 * Evaluation/Conclusion Part 1:** (Danny)
 * The experiment and the data, that of the tables and graph, suggest that our hypothesis was correct and our purpose was satisfied. **By determining the coefficient of kinetic friction between the block and the hallway floor, the weight of the block, the initial velocity of the block by using DataStudio and a photogate, and the distance the block travels for each throw, we found the relationship between the amount of work done by friction and the initial kinetic energy. As stated in our hypothesis, the experimental data showed that the initial kinetic energy and the work done by friction are the same, and are directly proportional. For instance, using the coefficient of friction we determined (with a 99.66% precision) to be 0.3469, and the distances traveled by the block in the 5 trials, we calculated the work due to friction in the 5 trials. For example, in Trial #1 the work due to friction was found to be 1.712 Joules. Also in trial #1, the initial kinetic energy, discovered using the initial velocity through the use of a photogate, was calculated to be 1.722 Joules, only a 0.57% difference. Similar results were consistently exemplified in the other four trials, whereas the initial kinetic energy was shown to be the same or close to the work done by friction. This is because the Law of Conservation of Energy states that final energy is equal to the sum of initial energy and work, which in this case is W = KEi, or work done by friction to make the object stop and be at rest is the same as the initial kinetic energy that it moves with. Thus, the purpose was satisfied in that we found the relationship between he initial kinetic energy and the amount of work done by friction, which confirmed our hypothesis of the two being directly proportional (equal).

There were certain errors with the experiment. While it did show overall consistency in proving our hypothesis of the directly proportional relationship between the initial kinetic energy and the amount of work done by friction, especially in Trials 1 and 3, with percent differences of only 0.57% and 0.90%. This demonstrates the equal and thus the directly proportional relationship between the initial kinetic energy and the amount of work done by friction. However, certain other trials had larger percent differences, especially Trial 5 which had a 7.96% percent difference. So, there was some margin of error. As for where the error occurred (shown in the percent difference column in the data table of Task B), it probably occurred when the initial kinetic energy and amount work done by friction were off, which was most likely due to an error in the amount of work done by friction where the distance of the block traveled, which was then plugged in the equation W= F * d * cosθ, and thus would have thrown off the value of the amount of work done by friction and therefore increased the percent difference between that value and the initial kinetic energy. This is where the error occurred, which could have resulted from various sources of error. First, there could have been an error in finding the amount of work done by friction. As aforementioned, the work done by friction was found by the equation F * d * cosθ. But in finding the distance, we sometimes would not throw the block straight but only accounted for the distance it was thrown, while it actually travelled both the vertical and horizontal distance (travelled the distance like a hypotenuse, but we only measured the length of one side, that along the tape measurer) and we also eyed the distance. This could have allowed for a small margin of error which may have skewed the results. In addition, the amount of work by friction could have been slightly changed if our coefficient of friction was off, which is possible because one source of error in actually finding the coefficient of friction could have been not pulling the block at a constant velocity which could have allowed for acceleration and thus changed the coefficient of friction. These sources of error could have allowed for the percent differences.
 * Evaluation/Conclusion Part 2:** (Danny)

1. The magnitude of work, done in this case by friction, is equal to the initial kinetic energy value. 2. The two are equal, and therefore directly proportional. 3. If more mass was used, the force of friction would increase. So, the magnitude of work done by friction and the initial value for Kinetic energy would also increase. 4. This would increase the coefficient of friction which also increases the friction force. So, the work done by friction and the value for initial kinetic energy would increase as well. 5. The coefficient of friction, force of friction, work done by friction, and initial kinetic energy value would all decrease.
 * Answers to Questions:** (Alanna)

i) To eliminate some error in this experiment, we could have increased the amount of data points we used. If we used different kinds of materials and surfaces, we could have further proved that work done by friction is equal to the initial kinetic energy with different coefficients of kinetic friction. ii) This experiment can be used to estimate the stopping distance for any object moving on a friction surface, like a car or a skier. But also, the concept that the kinetic energy expelled is equal to the force of work being performed in a given action is applicable in many instances. For example, it can be used to figure out how high an airplane must fly for its passenger to sky-dive and land safely on the ground.
 * Evaluation/Conclusion - Part 3**: Implications for further discussion (Alanna)