Group3_4_ch5

toc =Centripetal Motion Lab=

Part A - Lauren Barinsky Part B - Garrett Almeida Part C - Hella Talas Part D - Stephanie Wang

Determine the relationship between centripetal force and the variables of mass, radius, and velocity.
 * Objective:**

Mass- As the mass increases, the centripetal force measure will increase in magnitude. Linear direct relationship
 * Hypothesis:**



Radius- As the radius increases in size, the centripetal force will decrease in magnitude. inverse relationship



Velocity- As the speed increases, the centripetal force will increase in magnitude. Power fit direct square relationship




 * Procedure:**

We started the lab by assembling a device in which a stopper was attached to one end and a force meter was attached at the other end. A tube was held (as opposed to the string) when spinning so that only centripetal force is recorded, not tension. We used the force meter by connecting it to the computer via a USB link. To record our data, we had to change the y-axis to Force Pull-Positive. We tested three variables and in order to test these we had to keep two variables constant and test one variable at a time. For mass, we added more stoppers on the side with the stopper while keeping radius and velocity the same. To test for radius, we increased the length of rope above the tube and marked it with a marker to record the length while keeping mass and velocity the same. To test for velocity, we span the rope and stopper faster each time that we tested and kept radius and mass the same. We also used a stop watch to measure ten rotations of the string while spinning. We divided by ten to get the velocity it took for the stopper to go around a circular path once.

Video:

media type="file" key="Circular motion lab video.mov" width="300" height="300"


 * Data:**










 * Graph:**








 * Analysis:**

∑ F c = ma c ∑ F c = mv 2 / R

__Centripetal Force vs. Mass __ Looking at the equation, this graph should have a direct linear relationship. As mass increases, total force directly increases. The y intercepts for these graphs are 0 since there is no velocity, mass, or radius when the force is 0.

__Centripetal Force vs. Velocity __  In this graph, the centripetal force is directly proportional to the square of the velocity as seen in the equation, which also shows that the slope of the graph would be mass / radius. The graph should have a positive parabolic curve which is what we had expected, a direct square relationship. Although not very evident, our graph does seem to show this relationship.

__Centripetal Force vs. Radius __ This graph should have a negative parabolic curve which shows that the radius is indirectly related to the centripetal force; centripetal force = 1 / m. Although it is not clear, our graph shows this relationship.


 * Conclusion:**

Our hypothesis was correct. We said that as system mass increases, the net force also increases. Furthermore, we said that there is a linear relationship. As we found out in our lab, this is indeed the case. Also, we hypothesized that as the velocity increases, the net force also increases. We thought that this would make a parabolic graph. Our graph proved this to be true. Our final hypothesis says that as the radius increases, the net force decreases, since they are inverses of each other. This is correct, as we found out in our lab.

Our results for this lab were not excellent, as our r^2 value for the velocity vs centripetal force graph is .85. This means that our graph is only 85% accurate. For our other graph, which depicts radius vs centripetal force, we had to use last years data (credit goes to Ms. Burns). We got erroneous results for this part of the lab because our force sensor was set to "push" instead of "pull." Thus, we decided to use last year's class data. For our third graph, which compares mass with the centripetal force, we also got okay results that are not terrific. Since our results were not perfect, we had many sources of error. It is impossible to have a constant velocity because we cannot spin the string with a constant velocity. To fix this, we could have a machine spin the string around, since a machine probably has the ability to spin a string around at a constant speed. Also, we did not have an accurate measure of the radius. We measured the length of the string, but as it spun, it dropped down. Thus, what we had measured became only one component of the radius. To fix this, we could have measured how far down the string dropped, and used the Pythagorean theorem to obtain the actual radius. Also, timing proved to be a problem. The person timing had to pick a point to start measuring and count ten revolutions. The person timing could have stopped the timer when the string was a little bit to the right or left of the original starting location. Since even a one hundredth of a second counts in this lab, that could have made a very large difference. To mend this mistake, everyone in the group should have timed, and we should have taken the average of all our times.

=Minimum Speed Activity=

Garrett Almeida - Conclusion (D) Set-up (B) Lauren Barinsky - Data (A) Hella Talas - Calculations (C)


 * Measurements and calculations**

Individual Data - Trials were all done with a 50 gram weight.

Class Data-



Average of the Trials
 * Percent error**

( | 3.13 - 4.472 | / 3.13) x 100 = 42.88%
 * ( ** | Theoretical - Experimental | / Theoretical ) x 100


 * Conclusion**

In this lab, we were only able to attain velocities above that of the expected minimum velocity. This is because the velocity is supposed to be constant, however we were probably not able to do so due to human error. Also, the minimum velocity would account for some slack in the string. We were not able to do this as we would have had to find the exact velocity at which the string did not slack, but had no tension (this is not possible). The chances of doing this, is very slim. This is reflected in our percent error, a 42.88% error. This can be explained by what was mentioned above. Namely, keeping the radius the same, keeping a vertical circle, and exerting no tension on the string were all causes of error. Our data was also relatively close to the class average. There was a percent difference of 9.39%. As one can see by the class data, all groups did not record a value even close to the theoretical value of 3.13 m/s.

=Moving in a Horizontal Circle Lab= 1/6/12

Part A: Garrett Almeida Part B: Lauren Barinsky Part C: Lauren Barinsky Part D: Hella Talas


 * 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?


 * Hypotheses:**
 * 1) As the radius increases, the maximum velocity increases. [[image:Screen_shot_2012-01-06_at_9.42.50_AM.png width="89" height="30"]], so as one variable increases, one on the other side must increase.
 * 2) Banking an angle decreases the radius at which a maximum velocity is reached. Banking an angle allows for the weight force acting on the car to play a role in keeping the car traveling in a circular path.
 * 3) As the banking angle increases, the maximum velocity increases. [[image:Screen_shot_2012-01-06_at_9.42.54_AM.png width="122" height="25"]] so as any variable increases, one on the other side must increase.

The equipment used in this lab includes a rotational turntable, a power supply, a photogate, a mass, a banking angle, and a metric ruler.
 * Materials and Method:**

Each lab group was assigned a radius and recorded the results of 8 trials with the given radius. Our group used a radius of 0.2 m. We placed a flat mass at the 0.2 m line on the turntable and hooked up the device to DataStudio on the computer. We set the program to use the photogate to record the time it takes for the turntable to complete a revolution (period), shown under "Time Between Gates." We slowly increased the voltage on the turntable, making it rotate faster, while DataStudio was collecting the data. We stopped DataStudio when the mass began to slide off of the turntable and recorded the last time value as the period. We repeated this process for eight trials. We were left with eight values for the period when the mass was at its maximum velocity.

media type="file" key="Movie on 2012-01-06 at 11.36


 * Data:**

Our group collected the data for a circle of radius 0.2 m. We combined our data with that of the other groups in the table to get a maximum velocity for each radius.

A value of µ was calculated for each lab group using the equation.






 * Analysis**:

Percent error for exponent (B value):

Experimental µ: 0.529 µ derived from graph: 0.508 (derivation shown in question #2) Percent difference between the two:

//1. Discuss the shape of the graph and its agreement with the theoretical relationship between R and v.//

The maximum velocity is the y value R is the x value. The maximum velocity and the square root of the radius are proportional to each other, so the graph's trendline should have a power fit curve with an equation that follows the format. The theoretical B for a power fit curve is 0.5. Our equation is y=2.231x 0.4744, so our A value is 2.231 and our B value is 0.4744. To solve for µ, we can use the equation using the A value.

//2. Derive the coefficient of friction between the mass and the surface//. Or, using the A value from the graph:

//3. Compare your coefficient of friction with that of all groups doing this lab.//

Our µ: 0.529 Avg µ: 0.551

//4. A “car” goes around a banked turn.//
 * 1) //Find an expression for its maximum velocity, in terms of variables only.//




 * 1) //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?//

The maximum velocity for each radius value would be larger, so the A coefficient would be larger. This is because the normal force of the surface on the mass would be helping to keep the mass on a circular path.


 * Conclusion**:

Our hypothesis that the maximum velocity and the radius have a direct relationship was proven to be true through our data collected. Our graph shows that as the max velocity increases, the radius increases. Also, we predicted that a banked turn would decrease the radius and increase maximum velocity. We know this because the sharper the turn is, there’s a higher velocity. However, we did not conduct an experiment to prove this hypothesis.

 Our percent error between the coefficient of the graph and its theoretical value was only 5.12%. This means that we had extremely good results since it was less than 10%. In addition, our percent difference between our experimental and theoretical coefficient of friction was only 4.13%, which also show really precise results. Many possible errors could have occurred through human fault. For example, a mistake could have been easily made when trying to increase velocity of the turntable to maximum velocity. In addition, human reaction time plays an important role when clicking stop when collecting data on data studio. In order to address these errors, our group could have done more trials. In addition, we could have tested each persons reaction time in the group to see whose was the fastest and use that person to click the stop button on data studio. A real life application for this concept is when a car is in circular motion and is trying to avoid maximum velocity so the car does not skid.