Group6_6_ch5

Task B and D: Julia Task A and C: Jake
 * Lab: Moving in a Horizontal Circle **
 * __Objectives:__**
 * 1) What is the relationship between the radius and the maximum velocity with which a car make a turn?
 * 2) How does the presence of banking change the value of the radius at which maximum velocity is reached?
 * 3) How does changing the banking angle change the value of the radius at which maximum velocity is reached?


 * PrelabAssignment:**
 * 1) As the radius is increasing, the maximum velocity will increase as well. The square root of the radius is proportional to the maximum velocity, which can be supported by the fact that v= (Rµg) 1/2 . When the radius is increasing, the value of the equation to the right will be greater, and therefore so will maximum velocity.
 * 2) The presence of banking allows maximum velocity to be reached at a smaller radius. The angle provides greater balance, allowing for sharper turns.
 * 3) Increasing the banking angle will allow for balance at a smaller radius while decreasing the banking angle will cause the radius to be larger, for that is reaching the horizontal axis.
 * //Variables// || //Constant or Variable// || //How to Acquire information// ||
 * radius || r || meter stick/mark on turnable ||
 * angle || theta || protractor ||  ||   ||

We used the rotational turntable to find the max speed that the turnable can go without the mass flying off of it. The power supply allowed us to connect to our computer using data studio. The metric ruler was used to measure the exact size of the radius, which was 0.35 m. The photogate acted as a sensor to calculate the period on which the turnable went around. media type="file" key="Movie on 2012-01-06 at 15.17.mov" width="300" height="300" This video shows the turnable spinning, as it was in the experiment.
 * Methods and Materials:**


 * Data**:




 * Graph:**


 * Sample Calculations:**


 * Free Body Diagram:**

> > >
 * Analysis:**
 * 1) Discuss the shape of the graph and its agreement with the theoretical relationship between R and v.
 * 2) The shape of the graph represents the theoretical relationship between radius and velocity. Our graph of R vs. V uses the general equation V=( μg) 1/2 R 1/2 where μg remains constant. Therefore, it fits our equation of 2.2232x .0477, where 2.223 is (μg) 1/2 , R changes along the x axis, and .477 is close to .5, accounting for experimental error. The shape of the graph is a positive trend, showing that as radius increases, so does velocity.
 * 3) Derive the coefficient of friction between the mass and the surface.
 * 4) [[image:Screen_shot_2012-01-07_at_9.18.24_PM.png]]
 * 5) Compare your coefficient of friction with that of all groups doing this lab. (Be sure to post a data table with the class values.)
 * 1) Percent Difference from class
 * 1) Percent Difference from line
 * 2) [[image:Screen_shot_2012-01-08_at_4.07.00_PM.png]]
 * 3) A “car” goes around a banked turn.
 * 4) Find an __expression__for its maximum velocity, in terms of variables only.
 * 5) [[image:Screen_shot_2012-01-07_at_9.52.39_PM.png]]
 * 6) How do you think the graph would change if you performed the same procedure but with an angled surface, instead of the level surface we used?
 * 7) The banked curve would allow for a greater velocity, since friction would no longer be the only centripetal force. The Normal force would also contribute to the centripetal force, allowing for a greater velocity. On the graph, it would be the same relationship as this experiment. However, the like would be steeper, since the velocity would be higher, while the radii remain constant.

We predicted that the maximum velocity would increase as the radius value increases. We did find that this was correct because we saw through our data that as the radius increased in size, the average velocity did as well. For example, when the radius was 0.35 m, the velocity was 1.65 m/s and when the radius was 0.4 m, the velocity was 1.72 m/s. Although we didn't particularly test the banking angles in our experiment because we did use flat surfaces only, we would still keep the same ideas that we hypothesized in our original pre-lab experiment. In the graph, we had the equation y=ax b, and in our case specifically, y=2.2232x 0.4766. In this case, the x represented the radius while the y represented max velocity. Because v=(gRµ) 1/2, we knew that the b value must equal, theoretically, 0.5. We did get a percent error of 4.68%, which was only slightly off from the theoretical value. We were able to calculate µ because we knew that the a-value on our graph must be equal to (gR), so plugging in the variables that we knew, we found our µ value to be 0.540. The percent difference that we found for this value was 3.15%, which is extremely low, and proves that our experimental results were greatly accurate with little error. There was definitely some error found throughout the experiment, as proven through our percent error and percent difference. We do know that we had to manually stop the data table and using our reaction as the best signal as to when the mass fell off of the turnable, there was obviously a little error because it was hard to distinguish exact time, especially with reaction time. The changing voltage throughout the experiment from trial to trial could have affected results slightly, and the changes at different rates could have affected the mass slightly differently. We also were only able to use measurements to certain decimal points, so even something as simple as exact placement of the mass on the radius or time to the exact second could have slightly altered results, accounting for more error. Ways to decrease this error could be using some kind of sensor to sense when the mass fell off of the turnable, in order to get much more accurate results of velocity. We could have used a turnable which increased speed more constantly so that we didn't have to worry about our manual voltage changing messing up results. Lastly, we could have used more advanced measuring tools like finer rulers etc. to take down the measurements. Applications of this experiment to real life could include simple everyday activities like riding in cars, and this information is really important for understand how a car works when turning at different speeds.
 * Conclusion**: