Sunday, September 15, 2013

Mass vs. Period (spring IA)


Research Question
In this investigation the following question will be explored; how does mass effect the period of a spring?
IV and DV Statements
The independent variable is the mass that was added to the end of the spring, measured in grams. The dependent variable is the resulting amount of time it takes for the mass to complete one period, this will be measured in seconds.
Purpose
The purpose of this experiment is to determine whether or not the amount of mass added to the end of a spring will affect the length of the period. If the mass is found to effect the period, then the relationship between the variables will be explored.
Diagram: Apparatus Set-Up
The following is a diagram of the apparatus used in this investigation.
**Paper copy of diagram available**

Controlled Variables/ Constants
In order to increase precision and reliability- the same metal stand, spring, and meter stick(shown above) were used in each trial. The period was measured each trial from when the mass was dropped  to when the mass returned to that same spot. This start/stopping position was held constant at 40 cm above the table, and was clearly marked my the meter stick adjacent the metal stand. Additionally, the bottom of the spring, rather than the bottom of the mass, was used to judge starting and stopping position- so as to keep drop height consistent even though the masses used were slightly different shapes and lengths.  The meter stick also remained in the same place throughout the trials. The same spring was never removed from the apparatus during the investigation, therefore ensuring a consistent position of the spring, weight of the spring (47 grams), and k-constant. The units of measurement for time and mass (seconds and grams, respectively) remained the same. Finally, the technique for dropping the weight was held constant  by having the same experimenter drop the weight for each trial. For example, no force was added to the mass or the spring- it was simply released.
Justification: Range of IV and Number of Trials  
The levels of the independent variable range between 70 grams and 212 grams. The first IV level was set at 70 grams because when trials were attempted at a lower mass (50 grams) the period was to short to reliably time. The upper limit was set at 212 grams due to the fear that more mass would over-stretch and permanently damage the spring. There were five trials to test the dependent variable. Five trials were done to increase reliability of the data, in that the precision of the data can be judged. Additionally, if an outlier is produced taking the average of all five trials will increase the accuracy of that data point.
Procedure
 In order to collect the data below, the apparatus is set up as shown above in the diagram. A metal stand is placed near the edge of a flat table, to ensure the mass can complete a full period without hitting the table. The meter stick is secured, parallel to the metal stand, to mark the start/stop point. The spring is secured to the end of the metal arm, and the masses are weighed and hooked to the bottom of the spring.
The point where the bottom of the spring meets the top of the mass is lined up at the 40 cm mark. The first experimenter drops the weight, careful to simply release the mass without adding any additional force to the mass or the spring. As the weight is released, a second experimenter starts the timer, stopping it when the mass returns to the initial position. The time is recorded. This is repeated five times at each IV level.
Data & Processed Data
                                                                                                                                          
                                  |       Period ( +/- 0.005 seconds)           |              |  Statistical    |
|Mass (+/- 1.5 grams)| Trial 1| Trial 2| Trial 3| Trial 4| Trial 5| Average | Uncertainty |
|           70                    |  0.54   |  0.60   |  0.54   |  0.49   |  0.58  |  0.44      |    0.05           |
|          100                   |  0.63   |  0.69   |  0.72   |  0.62   |  0.74  |  0.68      |    0.05           |
|           141                  |  0.95   |  0.87   |  0.81   |  0.95   |  0.84  |  0.88      |    0.07           |
|           170                  |  1.00   |  1.09   |  1.02   |  1.00   |  1.01  |  1.02      |    0.05           |
|           212                  |  1.15   |  1.11   |  1.26   |  1.19   |  1.28  |  1.20      |    0.09           |

Uncertainty
    The measurement uncertainty for the mass is set at (+/-) 1.5 grams. This was done because each mass was measured individually prior to starting the trials. The scale was correct to the nearest gram, meaning it had a measurement uncertainty of (+/-) 0.5grams. In order to add the maximum mass(212 grams) to the spring three smaller masses were attached together at the end of the spring. When the uncertainty of all three smaller masses is added together, the measurement uncertainty of 1.5 grams is found.
    The measurement Uncertainty for the period is set at (+/-) 0.005 seconds because the timer recorded the time to the nearest hundredth of a second; Therefore, it can be assumed the timer has a measurement uncertainty of (+/-) 0.005 seconds. However, the statistical uncertainty -ranging from (+/-) 0.05 seconds to (+/-) 0.09 seconds- is much larger than the measurement uncertainty. This uncertainty most likely was caused by human error (slow reaction time in starting/ stopping the timer. The statistical uncertainty is found by finding the range of the data and dividing it by two. For example:
               Sample Calculations (Statistical uncertainty for the 212 gram IV level)
        1) The maximum (1.28 seconds) and the minimum (1.11 seconds) values are found.
        2) The range is found by subtracting the min. value from the max. value: 1.28s-1.11s= 0.17s
        3) The range (0.17s) is divided by two: 0.17s/2= 0.85s
        4) The uncertainty is rounded up (0.9 s), so it can be reported as only one significant figure
Raw Data Graph


This graph displays the average period at each IV level, no relationship has been found yet.

Linear Fit


 A linear fit (shown above) does not work for this data because while it fits easily through the error bars in the y-axis, it does not go through all the error bars in the x-axis. Additionally, with the linear fit there appears to be a y-intercept- suggesting that when there is no mass attached to the spring a period of approximately 0.12 seconds would still exist. The relationship is clearly not a linear one, and the graph appears to curve slightly as more mass is added. The horizontal parabolic shape lead to an attempt to linearize the data by taking the square root of the mass.
Sqrt(Mass) vs. Period



     In taking the square root of the mass that was attached to the spring, there is a clear relationship to the duration of the period. The uncertainty in the x-axis was reduced from the original (+/-) 1.5 grams, to (+/-) 0.75 grams. This is because taking the square root is equivalent to raising the masses to the 0.5 power. Thus, the uncertainty is multiplied by 0.5.
     The mathematical relationship between Period and Mass is that:
                    Period=  0.1206[seconds/sqrt(grams)] x [Sqrt (Mass)]

  Conclusion

     The period is proportional to the square root of x The slope of the linear line of best-fit in this graph means that approximately 0.12 seconds is added to the length of the period for every one (square root of gram.). In other words, as time increases, mass increases by a little less each time.
The y-intercept is assumed to be zero because the min/max slopes surround the origin. This makes sense because the square root of the mass is at zero when the mass is at zero,meaning there is no mass attached to the spring; and when there is no mass it is logical that the period is also at zero seconds. Hence, with no mass to apply force to the spring, it does not  stretch and there is no period.
     The biggest source of error was definitely human error in the reaction time when starting and stopping the timer. Much of the mistakes in timing showed up as random errors throughout the data. However, a source of systematic error in this investigation may arise in the IV levels. In the future, the spring's 47 grams of mass should be considered when graphing the mass against the period. Upon realizing that only the mass added at the bottom of the spring was counted in calculations, the label on the x-axis of the graphs was changed from simply "mass" to "mass attached to spring"
      In the future, it would be very beneficial to use a stronger spring that could withstand more mass. Thus allowing for a greater range in the IV and making the parabolic shape of the graph much more prevalent from the beginning. Additionally, the speed at which the masses completed the period made it  impossible to take accurate data. In the future the trials could be video taped and, using video analysis, the trial could be slowed down so more accurate readings could be taken. With a stronger spring and video analysis of trials the range in the IV could be much larger and the data collected (even on the very small masses) would be much more accurate.






Thursday, September 5, 2013

P= F/A

P=F/a – Real life-application
 
  1. When designing a needle for doctors to use, they aim to minimize the area of the needle so as to minimize the amount of force doctors must use to produce the necessary amount of pressure to break through a person's skin when administering a shot .
  2. When a diver enters the water after completing a dive they come down with the same amount of force. A diver must minimize the area of their body that first hits the water to maximize pressure when they hit the water (in order to break through the water easily. For example: If a person hits the water in a fully extended belly flop (large area) they will not hit the water with a lot of pressure and will stay on top of the water- very painful L In contrast if they enter the water with their pointed feet first, the small area exerts a large amount of pressure on the water- allowing the diver to easily penetrate the water and enter painlessly as well as gracefully (without a splash).  
My Family on vacation in chicago

Thursday, June 13, 2013

End if the year

Looking back over my the year...these last two topics were the hardest for me- but I think now I understand them. What I really need to study is vocabulary because on every single test my worst section is vocabulary. Also, I need to just go back over equations from the beginning of the year that I may have forgotten. An most of all I need to learn order I magnitude. I am really bad at that.

Thursday, May 23, 2013

DCP

·         )

Raw Data Tables:

Current (+/-  0.3 Amperes)
Voltsge
(+/- 0.1 Volts)
Trial #
Trial #
Trial #
Trial #
Trial #
Trial #
1
.2
.2
.2
.2
.2
.2
1.25
.25
.25
.25
.25
.25
.25
1.5
.3
.3
.3
.3
.3
.3
2
.4
.4
.4
.4
.4
.4
3.5
.75
.75
.75
.75
.75
.75

Current (+/-  0.3 Amperes)
Voltsge
(+/- 0.1 Volts)
Trial #
Trial #
Trial #
Trial #
Trial #
Average
0.25
.25
.25
.25
.25
.25
.25
0.5
.3
.3
.3
.3
.3
.3
1.0
.35
.35
.35
.35
.35
.35
2.0
.5
.5
.5
.5
.5
.5
3.0
.65
.65
.65
.65
.65
.65

Current Running Through Light bulb



Current Running through Resistor

The measurement uncertainty for the voltage was set at 0.1 Volts due to the difficulties achieving the exact amount of voltage desired using the variable resistor. The measurement uncertainty is set at 0.3 Amperes because the ammeter is marked to the closest 0.5 (Amp .) Therefore the data is rounded to the nearest 0.5 Ampere. 0.5 Amperes divided by two is 0.25 Amperes, then rounded to the closest significant figure the uncertainty is 0.3 Amperes.

  




The line on both graphs fit through all of the error bars, so both graphs are linear functions.The equation for the first graph (through the light bulb) is:
 Current= 0.1433 (Amps/Volts)  x Volts + 0.2166

The min/max lines on the second graph fall around zero, so it can be assumed that the y-intercept is zero. The equation for the line of the second graph (through the resistor) is:

Current= 0.2209 (Amps/Volts) x Volts 

Wednesday, April 10, 2013

DCP light lab


Number of light units in a16 cm²  box. (+/-2  light units)



Distance of card from light source (+/- 1 cm)
Trial #1
Trial #2
Trial #3
Trial #4
Trial #5
Trial #6
Average
Statistical
Uncertainty
(+/- Light units)
5 cm
81
100
81
90
74
70
83
15
10 cm
25
39
36
36
36
36
35
7
15 cm
22
25
23
21
22
22
23
2
20 cm
11
16
14
13
13
15
14
2.5
25 cm
9
12
10
11
12
11
11
1.5

In order to count the light units within the square, the length and width were counted. Due to the light units partially in the square, the length and width were both estimated to the nearest whole unit. Therefore, the measurement uncertainty is 2 light units. The statistical uncertainty was calculated for each trial by finding the difference in the range data points and dividing that values by two.  For example, in the first IV level the following calculations were used: (100-70)/2= 15. There was a 1 cm measurement uncertainty in the distance because the smallest unit marked on the ruler was one centimeter. Additionally, there is human error in marking out the distances and placing the card precisely on the marked distances each time.
Graph: Raw data
Graph: Raw Data
With the line of best fit put onto the graph, it is shown that the data is not linearly related (the line does not fit through the error bars) The Data appears to be an inverse relationship. 


I tried to linearize this function (in many different relationships) and the best fit seemed to be inverse. However, it still did not quite fit. I think I need to reevaluate my uncertainty. 






Never mind, I figured out how to linearize it :)

N













Monday, April 8, 2013

Post topic 2 check in

1. I feel good about free body diagrams and I do not really understand order of magnitude.
2. I feel good about momentum and impulse but I don't really understand power or efficiency.
3. Yes, I think that the little reddish/ orangey book and the remediation on your website are good study tools.
4. I think my diagrams and my procedures are very good. I think that I need to work on the uncertainty in my data tables & better organizing my ia (formatting.)
5. yes, I was not sure how it should look. Now I have a clear example of what I should do.
6. It's helpful to use the blog to get your feed back. However, I'm no sure the reflection posts are really that helpful for learning. (But it also doesn't hurt, so if it helps you then I guess it's a good thing)