Group+4

Lab 20: Levers -- Investigating Torque Lab: Investigating Torque Period 2 Lab Completed: 4/6/10 Due: 4/13/10 Group: Sean Barron, Nami Sumida, Mallory Harwood, and Sarah Kerin

Hypothesis:
 * Objective:

Materials:** Meterstick, pivot, knife-edge level clamps, 3 mass hangers, set of masses, unknown mass, balance, string, masking tape.


 * Procedure:

Data Tables:

Calculations:

Discussion Questions:

Evaluation/Conclusion:**

Lab 19: Rotational Kinematics Lab: Rotational Kinematics Period 2 Lab Completed: 3/23/10 Due: 4/6/10 Group: Sean Barron, Nami Sumida, Mallory Harwood, and Sarah Kerin


 * Objective**: To find the relationship between tangential velocity & radius and angular velocity & radius


 * Hypothesis**: As radius increases, tangential velocity increases because they are directly related, due to the equation v = wr (w = omega). Angular velocity and radius are inversely related because of the same equation.


 * Materials:** Turntable, disc with velcro tab, photogate with ports, data studio, ruler

1. Gather materials, set up record and data studio 2. Set up data table 3. Measure distance of tab and radius 4. Hold photogate above record 5. Start record and record time in photogate using speed of 78 rpm 6. Repeat steps 4 and 5 for 4 other radii measures 7. Start record at 45 rpm 8. Hold photogate above record and record time in gate for .173 m radius 9. Repeat steps 7 and 8 for 4 other radii 10. Start record at 33 rpm 11. Hold photogate above record and record time in gate for .173 m radius 12. Repeat steps 10 and 11 for 4 other radii 13. Start record at 16 rpm 14. Hold photogate above record and record time in gate for .173 m radius 15. Repeat steps 13 and 14 for 4 other radii 16. Calculate tangential and angular velocities 17. Graph tangential velocity vs. radius
 * Procedure:**

Data Table 1: 78 rpm Data Table 2: 45 rpm Data Table 3: 33 rpm
 * Data:**

Data Table 4: 16 rpm

Data Table 5: Percent Error of Angular Velocity

Graph: Relationship Between Radius and Velocity for a Disk of Different RPMs


 * Calculations: (78rpm, trial 1)

Tangential Velocity = d/t = 0.02/0.0125 = 1.6015 m/s

Theoretical angular velocity = rpm >> rad/s = (78)(2)(3.14158)/60 = 8.168 rad/s

Actual angular velocity is the slope of the graph

Percent Error = (|theoretical - actual|/theoretical)(100) = ((8.168-8.927)/8.168)(100) = 9.291%

Discussion Questions:**

1. What happens to tangential velocity as the radius increases? As the radius increases, tangential velocity increases, as evident in the graph which has a positive linear slope. Tangential velocity and radius are directly proportional.

2. What happens to angular velocity as the radius increases? As the radius increases, angular velocity remains constant. This is because angular velocity simply depends on the size of the angle the object is moving around, which is unaffected by the size of the radius.

3. What does the slope of each line indicate? The slope of each line indicates the angular velocity in radians per second.

4. Why didn’t we measure the velocity by measuring the period and circumference? We didn’t measure the velocity by measuring the period and circumference because this would have given us an average velocity, as supposed to an instantaneous velocity, which is what we wanted for this lab.

5. Since we can convert everything to linear anyway, what you suppose is the point in using angular quantities? The point of using angular quantities instead of linear is to be able to measure, calculate, and understand motion of an object from a different perspective. Thus, we have knowledge that goes beyond the object’s simple, translational motion.


 * Evaluation/Conclusion:**

The purpose of our lab was satisfied. We found the relationship between tangential velocity and radius and angular velocity in radius. As the radius increases, tangential velocity increases and angular velocity decreases because of the equation linear velocity equals radius times the angular velocity. Our hypothesis was correct, this was exactly what we thought should have happened. For example, in our data you can see (in the 78 rpm table) that as the radius decreases from 0.173m to 0.04m so does the tangential velocity, from 1.6015 m/s to 0.3540 m/s. This shows a direct relationship between the two.

For the most part, the percent error increased as the revolutions per minute decreased. This is because it was harder to get accurate data when the tab was moving more slowly. At 78 rpm our percent error was 9.29, at 45 rpm, our percent error was 6.01, at 33 rpm, our percent error was 6.76 and at 16 rpm, our percent error was 14.24. Our average percent error was 11.78%, which although not under 10%, is still fairly accurate. However, our actual angular velocity is consistently greater than our theoretical angular velocity. Although our actual velocity was slightly greater, because it was consistent throughout our experiment, it was probably due to the errors that occurred in this lab. Because our error is consistent it is probably due to the same source throughout. There were many reasons why our percent error was larger than expected. First off, it was hard to hold the Photogate steady. Therefore, we may have moved the Photogate, which couls have significantly impacted our data. This problem could have resulted in the tab taking longer to go through this moving Photogate. Our percent error could also have been due to the inaccuracy of our measurements. Our measurements could have impacted our data because if our measurement for the tab was too large, then our resultant actual velocities would have been greater than they theoretically should have been. Also, if our measurements for the size of our radius were inaccurate, then this would create errors in our values for tangential and angular velocity as well. It was difficult to retrieve the data for the shortest radius distance. It was hard to hold the Photogate over the rotating disc. The wire on the Photogate also occassionally got caught onto the disc.

To decrease percent error, there are changes that could definitely be made to the lab. For one, instead of us unsteadily holding the Photogate, we could find a way to attach it somewhere so that there is no extraneous motion involved. One real life application, in which knowing the relationship between both angular and tangential velocity and the radius is necessary, is in carousels. The radius for horses closer to the center is smaller than the radius for horses on the outside of the circle. Thus, while the angular velocity is the same because all horses are traveling the same amount of degrees around the circle, the tangential velocity is different. For the horses on the outside, the tangential velocity is greater because they are traveling a greater distance than the horses on the inside in the same amount of time. It is also applicable in track races. The person on the outer lane has to run a greater distance, or run with a greater speed in order to go the same distance as someone running on the inner lane. However, both runners are still running with the same linear speed.

Lab 18: Ballistic Pendulum Lab: Ballistic Pendulum Period 2 Lab Completed: 3/16/10 Due: 3/23/10 Group: Sean Barron, Nami Sumida, Mallory Harwood, and Sarah Kerin


 * 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 to one another. This is evident by the Law of Conservation of Momentum, which states that momentum is conserved throughout a collision.


 * Materials:** Projectile Launcher and steel ball, Plumb bob, meter stick, clamp, balance, ruler, carbon paper, printer paper


 * Procedure**:
 * 1) Set up projectile launcher
 * 2) Measure the height of the launcher from the mouth of the launcher to the floor
 * 3) Load the ball to medium range
 * 4) Launch the ball 5 times and record horizontal distance using carbon paper (as done in previous projectile labs)
 * 5) Find average distances and use this number as the range in kinematics equations. Solve for time, then solve for initial velocity of the ball
 * 6) Attach the ballistic pendulum to the launcher
 * 7) Launch the ball once, it should launch into pendulum and swing upwards
 * 8) Move the angle measuring needle on the ballistic pendulum 2-3 degrees less than the first launched
 * 9) Launch 5 times
 * 10) Take average angle measure
 * 11) Measure length of pendulum
 * 12) Use work energy and conservation of energy equations to solve for velocity
 * 13) Compare velocities and calculate momentum

Data Tables:

 * Data Table 1:** Data for a Ball Launched into a Projectile




 * Data Table 2**: Data for Ball Launched into a Ballistic Pendulum Using Conservation of Momentum




 * Data Table 3**: Percent Difference Between Initial and Final Momenta of Ball in Ballistic Pendulum


 * Data Table 4:** Percent Difference Between Velocity of Ball in Projectile and Initial Velocity of Ball in Ballistic Pendulum

mass of pendulum = 0.245kg mass of ball = 0.066kg length of pendulum = 0.3m angle of elevation = 40.9degrees
 * Calculations:**

Finding velocity with projectile:

Find percent difference: Percent difference = [abs (final-initial)/final]*100 [abs (0.346-0.313)/0.346] * 100 = 9.516%


 * Discussion Questions:**
 * 1) In general, inelastic collisions do not conserve kinetic energy while elastic ones do. In perfectly inelastic collisions, the object stick together and move as one and the final velocities are equal. In elastic collisions, kinetic energy is conserved and the velocities are equal but opposite.
 * 2) In the collision with the ball and the pendulum, it was an inelastic collision. This was because the ball was launched into the pendulum, and both the pendulum and the ball moved as one. The kinetic energy was not conserved. Momentum is conserved because it must due to the Law of Conservation of Momentum. Momentum is conserved from when the ball hits the pendulum to the maximum height.
 * 3) When the pendulum swings with the ball in it, the momentum is conserved. The Law of Conservation of Momentum states that the initial momentum is equal to the final. In the lab, the ball has the same initial and final momenta. The energy of just before the ball hits the pendulum and the energy of when it is at maximum height is not conserved. Since the collision is inelastic, the kinetic energies were not conserved therefore all energy could not be equal.
 * 4) KEbefore = (1/2)(m)(v^2) = (1/2)(0.066)(5.353^2) = 0.946 J
 * 5) KEafter = (1/2)(m)(v^2) = (1/2)(0.066)(1.136^2) = 0.0426 J
 * 6) KE lost = 0.946 - 0.0426 = 0.9034 J
 * 7) Percent loss = 0.9034/0.946 x 100 = 95.50%
 * 8) It is valid to assume that the kinetic energy was not conserved in this collision because it was inelastic and we did not expect it to be conserved.
 * 9) M/(m+M) = (0.245)/(0.066+0.245) = 0.788
 * 10) When doing the virtual simulation I was allowed to conclude two things. When increasing the balls mass, the velocity increased, which meant that the height the pendulum traveled was much higher. This was because the more mass an object has, the more force and momentum it has. So when it hit the pendulum it moves higher. But, when I increased the mass of the pendulum, the height decreased significantly. This was because it is harder to move a heavier object up against gravity.
 * 11) The difference between the velocities is not very significant. It is only slightly different. The percent difference ranges from 8-13%. For example, in the first trial of both, when calculated with projectiles the initial velocity was 4.742. When calculated with momentum it was 5.241. This created about a 9% difference. This is not very different. The factors that could have contributed to this difference is with the observations. When the pendulum swung upwards the angle was estimated and when the arm was placed back down it could be in a different position. Also, when the pendulum was straight down it may not have been exactly vertical at rest. There was also friction on the arm of the pendulum, and this could have slowed down the pendulum, decreasing its height. There was also confusion about the pendulum's center of mass. Therefore, we had to estimate where the center of mass was, and then use that estimation in our calculations. If I were to build a ballistic pendulum that would give better results, I would be one with less friction between the surface, and so it would have a more accurate reading of the angle of elevation. Also, the center of mass would already be labeled on the pendulum.
 * 1) The difference between the velocities is not very significant. It is only slightly different. The percent difference ranges from 8-13%. For example, in the first trial of both, when calculated with projectiles the initial velocity was 4.742. When calculated with momentum it was 5.241. This created about a 9% difference. This is not very different. The factors that could have contributed to this difference is with the observations. When the pendulum swung upwards the angle was estimated and when the arm was placed back down it could be in a different position. Also, when the pendulum was straight down it may not have been exactly vertical at rest. There was also friction on the arm of the pendulum, and this could have slowed down the pendulum, decreasing its height. There was also confusion about the pendulum's center of mass. Therefore, we had to estimate where the center of mass was, and then use that estimation in our calculations. If I were to build a ballistic pendulum that would give better results, I would be one with less friction between the surface, and so it would have a more accurate reading of the angle of elevation. Also, the center of mass would already be labeled on the pendulum.


 * Evaluation/Conclusion**:

In completing this experiment, our objective was definitely satisfied, as we were able to find the relationship between the initial and final momenta of a ball fired into a ballistic pendulum. In terms of velocity, percent difference ranged from 8% to 13%. For example, in trial 1, we got an initial velocity of .313 m/s and a final velocity of .073 m/s, resulting in a 9.5 percent difference. This makes sense because the collision was elastic and thus, Kinetic Energy was not conserved, resulting in different initial and final velocities. We also found the percent difference for the initial and final momenta of the ball. For each trial, this was less than one, proving our hypothesis was correct. The initial and final momenta of the ball are equal because momentum is conserved throughout a collision, as stated in the Law of Conservation of Momentum. An example would be for trial one: the initial momentum was .3459 kg/ms, the final momentum was .3458 kg m/s, resulting in an extremely small percent difference of .02%.

Theoretically, the two velocities and momenta that was retrieved from the projectile and the ballistic pendulum should have been the same; however, we calculated that there was an 11.286% difference between the averaged trials. The individual trials’ percent differences were also similar, between 9% and 13%. From this we can conclude that there was a significant percent difference, and that there were sources of error that contributed to this difference. One source of error may have been the friction between the ballistic pendulum and the pendulum and the surface. This was an issue when we measured the angle of elevation. Although we first measured it, and then only put it back a couple of degrees from that initial angle in order to reduce the friction as much as we could, there was still friction present between the needle and the surface. Another source of error may have been the presence of air resistance. During the projectile, there may have been some wind or air resistance that slowed down the ball. We also only used 5 different trials, so there may have been some error there, and if we had used perhaps 10 trials, we may have gotten a better value for the average. Also, we did not calculate the exact center of mass. We estimated that the center would cause the height of the pendulum to decrease, so we took off some distance from our calculations; however, regardless, it may have caused some error in the calculations.

This lab can be applied to collisions that occur in real life. For example, inelastic collisions in general are very important. Inelastic collisions can include car crashes, which consider seat belts and air bags. Understanding inelastic collisions are very important in determining the cause and effect of car crashes. Ballistic pendulums are not that common in real life scenarios. The launched ball can be compared to a cannon being launched. A pendulum can be compared to a swing or a pendulum on a clock. These two ideas can be compared separately but hard to be compared to real life together.

Also, if we were to improve the results in our lab, we would probably improve the equipment that we used, or add more steps to yield a more accurate conclusion. A major source of error was the center of mass, so if we were able to redo the lab, we would accurately calculate the center of mass, not just estimate its location. Also, we would use equipment with no friction (theoretically), but since friction is always present, we would find a way to measure the friction between the pendulum and the surface, and take that into account in our calculations.

Lab 17: Energy of a Projectile Launcher Lab: Energy of a Projectile Launcher Period 2 Lab Completed: 2/9/10 Due: 2/23/10 Group: Mallory Harwood, Sarah Kerin, Nami Sumida, Sean Barron

=Purpose/Objective: We are trying to figure out the relationship between the elastic potential energy of a compressed spring, the kinetic energy at the initial projection and the potential energy at maximum height. = = = =Hypothesis: We hypothesized that all of these points will be equal. This is because of the law of conservation of Energy. This says that energy cannot be created or destroyed, it can only be transferred. Since this is all one system the energy will just be transferred so they must all be equal. = = = =Diagram:=



=Procedure:=

=

 * Methods:** In order to compare the relationship of potential energy, kinetic energy, and elastic potential for a ball shot vertically upward, you need to find the value for each separate energy and then compare them.=====

**Graphs & Tabl****es:**

Data Tables:
Data Table: Potential Energy

DATA TABLE: Kinetic Energy

DATA TABLE: Finding spring force constant

Graphs:
GRAPH: Spring Force Constant



Sample Calculations:
Using Trial 1:

//To find Potential Gravitational Energy:// PEg = mgh PEg = (0.01)(9.8)(0.49) PEg = 0.0480 J

//To find Kinetic Energy:// v = d/t v = (0.0258)/(0.00837) v = 3.08 m/s

KE = 1/2mv^2 KE = (1/2)(0.01)(3.08)^2 KE = 0.0474 J

//To find Spring Force Constant:// PEs = 1/2kx^2 PEs = 1/2(124)(0.03)^2 PEs = 0.0558 J

//Percent Differnce Between Gravitational Potential Energy and Kinetic Energy// ((.0478 - .0474) / .0478) x 100 .8 % difference

//Percent Difference Between Gravitational Potential Energy and Elastic Potential Energy ((.//0558 - .0478) / .0558) x 100 14% difference

//Percent Difference Between Kinetic Energy and Elastic Potential Energy// ((.0558 - .0474) / .0558) x 100 15% difference =Conclusion:=

Discussion Questions:
1. Why didn’t we calculate Work due to the spring or due to gravity?

We did not calculate work because you never need to calculate the work due to a spring or work due to gravity. Instead of calculating work you use the potential energy due to spring (elastic potential) and potential energy due to gravity (gravitational potential), which represent the amount of work done. Instead of calculating values for work, we calculated PEs and PEg in this lab.

2. How do you explain the relationship between PEs, Peg, and KE?

The values of energy for PEs, Peg, and KE are all equal because of the law of conservation of energy. Because all three of these forms of energy are occurring at separate points in the projectile launcher and because energy cannot be created nor destroyed, each value of energy must be the same. The diagram above represents the points at which PEs, KE, and PEg are present within the system. These three values of energy are equal as they each represent the total amount of energy in the system at a given point.

3. What do you think would happen if you used a ball with more mass?

If we used a ball that had more mass, each value of energy in our lab would have a greater value. This is because if a greater value for mass was put into each specific equation, then the total amount of energy would be raised. Also, if the ball being used had a larger mass, the values of energy would increase because it takes a larger amount of energy to move a larger ball. However, even though the specific values for each amount of energy would be changing, the relationship between all of them would still remain the same. The relationship between PEs, Peg, and KE would still remain close to equal even if the mass of the ball was increased.


 * Evaluation / Conclusion**

Our purpose was satisifed in this experiment, as we were able to establish the relationship between the elastic potential energy, initial kinetic, and gravitational potential. Our hypothesis was correct, as the amounts of all three forms of energy were very close to being equal to each other, as they should have been due to the Law of Conservation of Energy. The gravitational potential and kinetic energies were pretty much the same with a less than 1% difference. The elastic potential energy was a little further off from these two values, but this was not theoretically supposed to happen. This larger error is for reasons discussed in the following paragraph. This lab ultimately reinforced the Law of Conservation of Energy, showing how the type energy simply transforms at different stages, but the amount or value of the energy never increases or decreases.

The values of elastic potential energy, kinetic energy at initial projection, and potential energy at maximum height should have all been equal, as in this experiment, elastic was converted to kinetic, which was then converted to gravitational potential. As The Law of Conservation of Energy states, energy is neither created nor destroyed, but simply transferred. Thus, there was no destruction of energy and the amount of energy at each stage should be precisely the same. The percent difference between the values of Kinetic Energy and Gravitational Potential Energy is extremely small, at only .8%. This small difference resulted from the very accurate procedure and our precise calculations. On the other hand, the percent difference between elastic potential and kinetic energy and elastic potential and gravitational potential is much greater. There is a 14% difference between elastic potential and gravitational potential and a 15% difference between elastic potential and kinetic. This large difference is probably due to the fact that a different launcher and spring were used when calculating the spring constand than when finding potential and kinetic energy. Finding this spring constant was essential in finding the elastic potential energy. Our launcher and spring may have been defective compared to the ones Mrs. Burns used to find the spring constant, which consequently would have resulted in inaccurate results and a larger percent difference between the elastic potential energy and both the kinetic and gravitational potential energies. Also, other sources of error were when we measured the potential energy. We eyeballed the distance it traveled by putting a meter stick next to the launcher. This method was not a suitable method for finding accurate measurements. Also, we did not have a method to find the exact initial velocity of the ball, for finding the kinetic energy. Instead, we found the average velocity of the ball, which was very close to the intial velocity, but still, was not exactly the same.

In order to address the errors, there are several ways that we could have changed this lab. First off, we could have used a motion detector instead of eyeballing the distance with a meter stick, for measuring the height of the launched ball. Using a motion detector would have given us an exact and much more accurate value for the height of the launched ball. Another way that we could have addressed the error in our lab would have been if we found the spring energy of the launcher for the same launcher that we used in our experiment. Because every launcher is slightly different, and the launcher that the measurements were taken from was different than our own, we had a large value of error. If we had measured the elastic potential of the launcher we used in the rest of the lab, our error would have been significantly smaller. Another change we could have made in order to address the lab would have been to find the exact initial velocity at the mouth of the launcher instead of finding the average velocity through the photogate, which slightly changed the value of velocity and further increased our error. A relevant real-life application of this concept could occur in a cannon that is shot vertically. The physics behind the shooting of the cannon would be important to know because if you are able to find out the spring potential of the spring-powered cannon, then you are also able to figure out how high the cannon will go in addition to the velocity of the cannon. These calculations would be very important in providing a safe-environment for the cannon. Overall, finding the relationship between kinetic energy, potential gravitational, and elastic potential would be very useful in many real-life examples of spring-powered launchers.

Lab 16: Work Done by Friction Lab: Work Done by Friction Period 2 Lab Completed: 2/2/10 Due: 2/9/10 Group: Mallory Harwood, Sarah Kerin, Nami Sumida, Sean Barron

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

Hypothesis:
If there is more kinetic energy, then there would be more work because initial kinetic energy and amount of work done by friction have a direct relationship. This is true because if an object goes faster, there needs to be more work done by friction in order to stop it.

Procedure :
1. Materials: block of wood, Force sensor, Data Studio, motion sensor, tape measure (10m), string 2. Find the friction force by graphing the coefficient of friction 3. Set up the motion detector about 5m in front of where you will be throwing the block 4. Throw the block of wood (as if you are bowling) 5. Using Data Studio and the motion detector, graph the motion of the block. 6. Using the v-t graph, find the acceleration (the slope of the graph) 7. Measure the distance that the block traveled with the ruler. 8. Using kinematics, find the initial velocity 9. Calculate the kinetic energy with the kinetic energy equation 10. Find the work done with the work equation W = (F)(d)(cosθ) 11. Compare the two values and find the relationship between the two Data Tables:** Data Table: Coefficient of Friction Table Coefficient of Friction Graph
 * Graphs & Tabl****es:

Data Table: Work and Kinetic Energy of Wooden Block Thrown Down a Hall
 * Trial || Distance (m) || Mass (kg) || Final velocity (m/s) || Initial velocity (m/s) || Kinetic energy (J) || Friction force (N) || Work (J) || Acceleration (m/s^2) ||
 * 1 || 2.340 || 0.198 || 0 || 3.6199 || 1.2973 || 0.66 || -1.5396 || -2.80 ||
 * 2 || 1.494 || 0.198 || 0 || 3.0435 || 0.9170 || 0.66 || -0.9830 || -3.10 ||
 * 3 || 1.720 || 0.198 || 0 || 3.2970 || 1.0762 || 0.66 || -1.1317 || -3.16 ||
 * 4 || 1.375 || 0.198 || 0 || 3.1769 || 0.9992 || 0.66 || -0.9047 || -3.67 ||
 * 5 || 1.470 || 0.198 || 0 || 3.0480 || 0.9197 || 0.66 || -0.9672 || -3.16 ||

Sample Calculations:
Sample Calculations for Trial 1:

To find the initial velocity: vf^2=vi^2 + 2ad 0 = vi^2 + 2(-2.8)(2.340) 13.10 = vi^2 vi = 3.17m/s

To find the initial kinetic energy: KE = 0.5mv^2 KE= (0.5)(0.2)(3.6199) KE = 1.2973J

To find normal force:

To find the friction force: (using trend line equation To find the amount of work done by friction:


 * Percent Difference:**

Sample Calculations
Trial 1: [1.2973-(-1.5396)] / (1.2973) x 100 = 15.74%

=Conclusion:= Discussion Questions: 1. How does the magnitude of work compare to the kinetic energy? Theoretically, the two are supposed to be the same; however, the two from our experiment were off by a small percent.

2. How do you explain the relationship between the work done and the kinetic energy? Theoretically, the two should be equal to each other. Because motion only exists, the energy required to move the object is the same thing as the force applied or the work done to cause the motion.

3. What do you think would happen if you used a block with more mass? If we increased the mass, it would make the normal force of the floor onto the block greater, which would then increase the friction force, due to the coefficient of friction equation. Because of a greater friction force the work would also be greater, which would also mean a greater kinetic energy. We could also use the kinetic energy equation to see that mass and kinetic energy are directly related, so increasing the mass would mean increasing the kinetic energy required.

4. What do you think would happen if you used a rubber block instead of wooden block? There would be more friction. The work would consequently be greater and we would require a greater kinetic energy to slide the block the same distance.

5. What do you think would happen if you did this experiment on ice instead of on the tile floor? There would be much less friction if this were experimented on ice. As a result, the work done and the kinetic energy would be much less as well. Also, the block would travel a greater distance with a smaller applied force. Theoretically, if there were no friction, the block would continue to slide forever, until another force acted upon it.

**Evaluation/Conclusion**:
In this experiment, our purpose was satisfied. The purpose of this experiment was to find the relationship between initial kinetic energy and the amount of work done by friction. According to our data table, as the magnitude of initial kinetic energy increases, the magnitude of work done by friction increases as well. From looking at our data we realized that the magnitude of work and kinetic energy were very close. They were theoretically supposed to be the same; however, we had some large error within our experiment. Although we hypothesized that the two values would have a direct relationship, we did not hypothesize that the two were supposed to be equal to each other. Looking back on the experiment, it makes sense that the two values should be equal because the energy required to move the object is equal to the work done to cause this motion. This would be true because the only energy present is initial kinetic energy and work. Although our equation would show that kinetic energy would be equal to a negative value for work, we only compare the magnitudes of both values and do not take direction into account. The magnitude for our average kinetic energy was 1.0419 and the average magnitude of our work was 1.1052. These produced a percent difference of 5.727%. Our values for percent difference were widely distributed and ranged between 5% and 16%. These large percent differences showed that our values for work and initial kinetic energy were very different which could be caused from some errors that are described below.

The error in this lab could have been caused by different aspects. When the cart was tossed in a bowling motion, the motion detector could have not captured the whole time. This is because it was not always thrown in a perfect line. Another source of error is when calculating the distance. Since it was not thrown in a straight line path the distance was not exact. We used our finger to measure from the beginning of the cart to the meter stick in which the significant figures could have been slightly off. Thus, this would affect the work equation, velocity and several other aspects. Another source of error is where we threw the block. We eye-balled this location, so every trial may not have started at the same place. This error may have affected the distance that we measured. This source of error is due to our equipment and human error and could not be fixed unless other distance measuring devices were used in the lab.

It was very difficult to use the motion sensor in this lab. Instead of the motion sensor, if we were able to use a stop watch or a Photo-gate timer that would have more accurately measured the time of even acceleration, our results would have been more accurate. We could have also benefited from having a better way of measuring the distance. We eye-balled the distance, so if we had a better method, we would have been able to more accurately find the distance that the block traveled. We also could have had more data in finding out the coefficient of friction. More trials in both finding the friction force and the experiment in general could have improved our results as well.