Tom,+Rory,+Tyler,+Richie

toc =__Moving in a Horizontal Circle Lab__=

Tom, Rory, Tyler, Richie Period 4 Due: 1/24/11

__**Purpose:**__ To understand the effect of a banking angle on an object that is moving in a horizontal circle.


 * __Hypothesis:__ A-** On an unbanked surface, the higher the maximum velocity, the larger the radius must be.
 * B-** On a constant banking angle, as the maximum velocity increases, the radius will increase.
 * C-** As the angle of the bank increases, the radius needed to have the object stay on the bank at its maximum velocity decreases.

__**Procedure:**__ media type="file" key="Movie 21 rj.mov" width="300" height="300" 6. Repeat step 5 with varying angled block 7. Once the distance of the penny is marked trace the block and measure both the angle and the radius of the circle in which it was traveling. __**Data**__**:**
 * 1) Obtain a record player, penny, stop watch, spool of fishing line, circular plate, tape, and wooden wedges ranging in angles.
 * 2) Tape the spool of fishing line to the record player and then tape the spool to the circular plate.
 * 3) Turn the record player on to 76 rpm and time the rotations for a minute so that we can see if it is actually spinning at 76 rpms.
 * 4) Next attach the wooden wedge to the plate and place the penny onto the wedge
 * 5) Start the record player on 76 rpm and see if the penny falls off. If it does lower the penny, if it does not the raise the penny until it falls off.



As the banking angle increases, the radius decreases.

(Graph of objective one taken from Jae, Jessica, and Danielle) As depicted in this graph, as the velocity increased on an unbanked surface, the radius did as well.

(Graph of objective 2 from Sean, Eric, Chris, and Phil) As the velocity increased on an constant bank, the radius increased.

__**Calculations:**__ The µ is used thanks to the work of Ani, Rachel, Ariel, Sammy

As the object (in this case, a penny) got further from the center on a banked angle, the harder it was for the object to remain on the record player. This is because as it got further from the center, its velocity increased. As the velocity increased, friction had less control over the object. At a certain point on each angle, the object would end up sliding off because the force pushing the penny away from the center becomes greater than the friction holding the coin on the banked surface. It is interesting to compare this to a car on a banked angle for an off or on ramp. After a certain speed, one would not be ab__l__e to maintain traction with the road and the car would slide off. Different banking angles allow for different speeds. For example, the smallest angle would allow for the smallest velocity before the object would fall off. Conversely, the largest angle allowed for a relatively high speed before it would slide off. The larger the angle the greater the friction was that held the penny on the surface therefore it took a much greater velocity to create a force larger than friction pushing in the opposite direction away from the center of the circle. While it is true that an object moving to fast for the angle of the bank will slide of, the opposite is also true, meaning that if the object traveling on the bank is going to slow then it will slide down the bank towards the center of the circle. The greater the angle of the bank, the greater the velocity of the object must be in order to keep from sliding on the surface. Every angle has a minimum and maximum speed at which an object can travel around them without sliding up or down the bank. Also, as the angle of the bank increased the radius of the circle decreased. The penny was able to make shorter revolutions around the center on the surfaces of the larger angles. This is because the object must travel faster in order to stay on the surface of a greater angle, therefore it has to make shorter revolutions in order to maintain a high velocity.
 * __Analysis:__**

Each of our hypotheses were correct. For procedure 1, we did not get to witness the information first-hand, but based off of Jae, Jessica, and Danielle's graph, our hypothesis for procedure on was confirmed. On an unbanked surface, as the velocity increased, the radius did as well. For procedure 2, our group borrowed Chris, Phil, Eric, and Sean's data. Their graph also confirmed our hypothesis for the second procedure. With a constant banking surface, as the velocity increased, the radius also increased, as we hypothesized. Our hypothesis about the banking angles and its relationship to radius ended up also being confirmed. As the banking angle increased, the smaller the radius was before the object fell off. This was represented in the lab data and the graph above. But like any other lab, there were multiple places of error. Despite the lab being split up into three parts, the sources of error were universal between the parts. For one, the board that the sat on the record player was not completely flat. There were warps in the wood. If one were to put the board on a table, it would not rest flat. This could effect the maximum velocity in that if the object was almost at its limit and it reached the point of one of the mutations of the wood, it could cause it to slide off. This would affect our data for its maximum velocity just enough to give us incorrect data. However, it was the only board at our disposal. Secondly, the board did not spin consistently. Of course it spun at generally the same rate, but when we recorded its times, they would fluctuate up to two seconds of the given time on the record player. As a third source of error, the intervals in which the object was moved up to determine its maximum velocity was not as exact as we could have made them. If we moved the penny up in smaller intervals, better data could have been recorded. In order to improve this lab, a completely flat board would be necessary. Also, rather than using a record player, the use of an object that spins at a consistent speed would be critical. As for the exactness of the maximum velocity, smaller intervals is the only thing that could improve it. =**__Vertical Circle Lab__**=
 * __Conclusion:__**

Tom, Rory, Tyler, Richie Period 4 Due: 1/12/11

__**Objective:**__ To find the minimum and maximum velocity of an object moving in a vertical circle.


 * __Hypothesis__:** The greater the mass pulling on the string at the bottom of the circle the lower the velocity has to be to have the string break. Thus the lower the mass pulling on the string at the top of the circle, the higher the velocity has to be to have the string break.

__**Procedure:**__


 * Finding Maximum Velocity:**
 * 1) Cut of a piece of string (any kind) around a meter long.
 * 2) Tie a known amount of weight to the bottom of the string.
 * 3) Add more and more weight to the end of the string until the string snaps. (The amount of weight tied to the string when it breaks is the maximum tension of the string)
 * 4) Once you have the maximum tension, attach a much smaller amount of weight to the string and swing it around in a circle until the string snaps.
 * 5) While you are spinning it be sure to be timing how many rotations the weight makes before the string snaps and how long it takes.
 * 6) Using this information you can find the maximum velocity of the string.
 * 7) Repeat the above steps until a sufficient amount of data has been collected.


 * Finding Minimum Velocity:**
 * 1) Cut a piece of string (any kind) and measure the length of it (this is the radius of the circle)
 * 2) Hang a light mass that will not snap the string easily on the end of the string
 * 3) Spin the string with the weight on the end multiple times until you are able to spin it at a constant velocity at which there is no tension in the string at the top of the circle
 * 4) Count the rotations the weight makes in a certain period of time
 * 5) Measure this velocity with the acquired information (this will be the minimum velocity)
 * 6) Repeat the above steps until a sufficient amount of data has been collected.


 * Data:**


 * Free Body Diagrams and Calculations:**

//F////BD when the object is at the bottom of the circle// //FBD when the object is at the top of the circle//

The results of our lab prove our hypothesis correct. With higher velocities, less weight was needed to snap the string. However, there are many places where error could have been made. For instance, consider when trying to snap the string with mass alone. The data collected was not as exact as it could have been. At first, our group went up in 50 gram intervals. Eventually, we moved down to 10 gram intervals. The data could have been more exact if smaller masses were used. In the second part, where the mass was spun until the string snapped, it is possible that the string could have snapped early if it was spun faster than needed. In order to avoid an error such as this, the one spinning the mass and string would need to be extra careful, increasing speed little by little. Also, if too much slack was given, the mass could fall to the bottom of the circle. This could mislead the data, tricking us into thinking it snapped merely from circular motion alone. In the last part, it is very difficult to get the velocity just fast enough so that there is no tension at the top of the circle. If the velocity is too fast, tension would be added and would change the calculations. Also, if the velocity is too slow, the time it takes to complete 10 rotations would be slower, throwing off all the calculations. This can be resolved by using a tool or technology to spin the mass and string while having the ability to fine tune the velocity.
 * Conclusion:**

=**__Circular Motion Lab__**= Tom, Rory, Tyler, Richie Period 4 Due: 1/7/11


 * __Purpose:__** To obtain the relationship between the speed of the system on the centripetal force.


 * __Hypothesis__:** As speed increases, the the force will increase.

__**Procedure:**__
 * 1) Gather the materials, which consist of a force meter, a string, a rubber stopper, a stopwatch and some tape.
 * 2) Create a circle on the floor with a radius of .022 m out of tape.
 * 3) Next, measure out .022 m of the string.
 * 4) Weigh the rubber stopper and then attach it to the string.
 * 5) Tie the string onto the force meter and put tape around the knot so the it stays in place.
 * 6) Swing the force meter in the center of the tape circle until the string is perpendicular with the ground.
 * 7) While spinning the string use the stopwatch to see how long it takes the string to go around the circle 10 times.
 * 8) Repeat step six with varying speed four more times.

__**Data:**__


 * Trial || Force (N) || Radius (m) || Time (s) || Mass (g) || Velocity (m/s) ||
 * 1 || 0.5 || 0.02166 || 2.35 || 13.2 || 0.5791 ||
 * 2 || 0.282 || 0.02166 || 2.73 || 13.2 || 0.3985 ||
 * 3 || 0.4 || 0.02166 || 3.1 || 13.2 || 0.439 ||
 * 4 || 0.461 || 0.02166 || 2.59 || 13.2 || 0.5255 ||
 * 5 || 0.372 || 0.02166 || 3.31 || 13.2 || 0.4112 ||
 * 6 || 0.654 || 0.02166 || 1.62 || 13.2 || 0.84009 ||
 * || Force || Velocity ||  ||   ||   ||
 * || 0.5 || 0.5791 ||  ||   ||   ||
 * || 0.282 || 0.3985 ||  ||   ||   ||
 * || 0.4 || 0.439 ||  ||   ||   ||
 * || 0.461 || 0.5255 ||  ||   ||   ||
 * || 0.372 || 0.4112 ||  ||   ||   ||
 * || 0.654 || 0.84009 ||  ||   ||   ||
 * || 0.654 || 0.84009 ||  ||   ||   ||

This experiment had more error in it than most other labs. There were many places where the lab data could go astray. First, when we did the lab, we went on the assumption that when we were spinning it, it was horizontal to the ground. If it were not parallel to the ground, which is a very likely scenario, the force could be affected. A way to assure that the object being spun is horizontal to the ground is to get a device to spin the object at various speeds. But no such tool or device exists in the arsenal of equipment in the physics classroom, so other tools were called upon. Another area of error is the speed at which the object was spun. If the object was not spun with a relatively constant speed, the force could significantly be affected, throwing off the data. Once again, in order to solve this problem, there would have to be a device to spin it. With more advanced equipment, constant speed would easily be achieved. As well as these human errors, there are also some mechanical errors. For example, the force meter was not specifically designed for this specific experiment. It was designed to measure a pulling (or pushing) force parallel with the meter. In our experiment, the pulling force was not straight down, rather horizontal. This caused fluctuations in the data. A more accurate reading of the force could be acquired if a different kind of force meter was used (manual force meter [not used because it would be moving too fast to read] or a force meter designed for similar experiments). In addition, the force meter would occasionally render nonsensical data. Nothing could really be done about such a problem, other than retrying the data. Lastly is mathematical error, which exists in every experiment. If a calculation is off or a formula is written slightly wrong, it could change the entire experiment. In order to prevent this, the mathematics are checked and double checked to make sure there are no faults.
 * Conclusion:**