07-SEP-2016 Freefall Experiment to Calculate Gravity At 9.81 M/S^2

In this experiment we will drop a plumb bob down a sturdy column that stands 1.5 meters above the ground. With an electromagnet at the top to hold the plumb bob until we want to release it. When released it will travel down the column between to wires and a spark sensitive tape. A spark generator will mark the paper at intervals of 1/60th of a second and with this information we will make a distance vs time graph and a velocity vs time graph to calculate the rate of acceleration due to gravity.

After conducting the experiment we took the spark sensitive tape and took measurements at each mark left by the spark generator. With the distance and the time we created 2 graphs using Microsoft excel.

In the conclusion to this lab I believe our results were pretty good. A few things to take into consideration that could have brought our value of 9.58m/s^2 closer to 9.81 would be taking air resistance into consideration. Another situation that can effect our results is using the meter stick and the accuracy of measurements are not exactly precise. Overall this was an outstanding lab with some good results to some not so good results. One problem that I have with the results was the overall of

class results varied a lot.

Our relative difference

(9.58cm/s^2-9.8cm/s^2)/(9.8m/s^2)*100% = - 2.24%

Questions

Show that, for constant acceleration, the velocity in the middle of a time interval is the same as the average velocity for that time interval?

Vfinal=DeltaX-1/2at^2/t^2=134.9m/s

average velocity=Delta X/Delta t= (11.8cm-9.1cm)/(0.10s-.08s)=135cm/s

Describe how you can get the acceleration due to gravity from your velocity/time graph. Compare your results with the accepted value?

Delta v/Delta t = (Vfinal-Vinitial)/(Tfinal - Tinitial)   (46.7cm-21cm)/(0.25s-0.15s)=257cm/s

Describe how you can get the acceleration due to gravity from your position/time graph Compare your results with the accepted value?

When you graph your results and then conduct a linear fit which will give you the tangent line to the slope which is our acceleration due to gravity.

Here is the graph from the class data  which calculated standard deviation of the mean.

One thing noticed in the class data for the value of g was all of them were under the 9.8m/s^2.

All of the class except for one tables results landed in the 68% within the accepted values.

I believe all of the error in this lab is measurments. which are systematic errors if we had a more precise way of measuring I think the results would be extremely different.

The purpose of the second part of this lab was to calculate the class values and how far from the actual value of g which is 9.81m/s^2.

29-AUG-2016 Inertial Pendulum Relationship Between Mass and Period

In this experiment we will be trying to find the mass of object using the relationship of known masses and period with the use of a pendulum.

To begin this lab we will collect data specifically the period from known masses. We will use this data to come up with a relationship between mass and period. Using the slope that was formed from the mass of our known objects we can now use the formula T=A(mass+Mass(tray))^n. After a little algebra this equation will now become (T/ln(A))^(1/n)-Mass(tray)= the mass of the unknown object.

The aparatus we will be using in this experiment is a mounted pendulum that sways from left to right. We will also be using a a photogate and the application of logger pro to collect the period of the pendulum with the known weight. We will use this set up to collect data from several known weights to allow us to achieve an effective mass and period relationship.   This is how our set up looked.

Now using a data table we collected the mass of an object as well as the period it took that object to complete one cycle. In order to keep everything uniform we collected 15 seconds of each mass and then took the average period in those 15 seconds. Here is a copy of our data table.

Now we took this data and created a graph with ln(mass+mass(tray)) on the x axis and ln(seconds) on the y axis. This data will be used to calculate our slope. We will adjust the weight of the tray a little bit to try and achieve a correlation of 1. In this step the closest you may achieve is .999 and if so we need to create a low limit as well as a high limit. So for the weight of our tray to achieve this is a low limit of 240g and a high limit of 300g. here is a graph of our lower limit as well as higher limit.

The information needed in these graphs are the y-intercept and the slope which we will need in our calculations for the mass of the unknown.

A = y intercept      n = slope      T = period (s)       Mass(tray)=(upper limit 300) or (low limit=240) 

After collecting this data we will now collect the period of our unknown mass objects

T tape dispenser = 0.6198(s)

T stapler = 0.4974(s)

Here are the results of our calculations to find the unknown mass using the period. The following equation was used to calculate the mass. The objects that were used was a tape dispenser and a stapler. The period of the two objects are as follows.

T tape dispenser = 0.6198(s)

T stapler = 0.4974(s)

(T/ln(A))^(1/n) - Mass(tray) = Objects unknown mass

Upper Calculations:

tape dispenser (0.6198/0.00624)^(1/.6740) - 300 = 618.34(g)

stapler             (0.4974/0.00624)^(1/.6740) - 300 = 362.59(g)

Lower Calculations:

tape dispenser (0.6198/.01125)^(1/.5924) - 240 = 629.08(g)

stapler             (0.4974/.01125)^(1/.5924) - 240 = 359.48(g)

actual mass using a scale:

tape dispenser = 625(g)

stapler = 369(g)

Conclusion:

Although our calculations were close I found our results to be very interesting. One of the most important thing to keep in mind during this calculation is where you place the object on the pendulum which will affect your results tremendously. After calculating our results the tape dispensers actual weight fell between our calculations but the stapler was out by about 6/7(g). This could be affected by air resistance and exactly where we placed the stapler on the pendulum. Clearly this lab shows that there is in fact a relationship between the mass of an object and the period it takes that object to complete one cycle.