acceleration of gravity on an inclined plane

Purpose: The purpose of this lab was to determine the effect of gravity on an object traveling up and then down an inclined plane, while gaining further experience with the graphical analysis software. Tools used included the logger pro software, a motion detector, aluminum track, ballistic cart, carpenter level, meter stick, and a wooden block, all shown under equipment needed you will see all the tools we needed for this lab.The ramp was setup at an incline with the wooden block, and carefully leveled. We then measured the change in height of the two sides, to the horizontal length of the inclined ramp. 

           

Equipment Needed:


lab pro interface

motion detector




carpenter level

wood block/ballistic cart/aluminum track



Procedure:

1.      Connect LabPro to the computer with the LoggerPro software and the motion detector to the DIG/SONIC2 port on the LabPro. Turn on the computer and load the LoggerPro software by double clicking the corresponding icon located within the PhysicsApps folder. Locate and open the file named graphlab; it will be used to set up the computer for collecting the velocity and acceleration data in order calculate the lines of best fit, thereby calculating the acceleration of gravity using the formula "gSinθ=(a1+a2)/2". Double-click on the Mechanics folder and then proceed to open the file by double-clicking it.

2.      Incline the end of the aluminum track by using the wood block as a wedge. Place the wood block roughly at the 50cm mark on the track. Use the level to make sure that the track is level. Once level, calculate the angle of inclination using basic trigonometry (calculate the heights of the track at both ends, subtract the smaller value from the bigger value, and then take the inverse sin of the result as seen in Figure 1).

3.      Place the motion detector at the upper end of the track facing down toward the lower end. Start with the cart at the lower end of the track and gently push the ballistic cart toward the motion detector until it is just outside 50cm from the motion detector. Make sure to stop the cart before it crashes into the track to prevent damage to the cart or track.

4.      Start data collection after the cart leaves your hand and observe both the position and
velocity graphs simultaneously by having two windows open (one above the other). Select suitable scales for both vertical and horizontal axes to best show the motion of the ballistic cart. Properly label the graphs with titles, units, and other relevant information. Repeat the trial until the graph looks like a consistent curve.

5.      Once an appropriate curve has been acquired, use the Logger Pro software to take a virtual snapshot of the slope of the curve v vs. t by selecting a range of times that represents the motion of the ballistic cart going up the incline. Choose the "Analyze/Curve Fit" option to fit the selected portion of the curve to a linear function of time. Repeat this process for when the ballistic cart is returning down the incline.

6.      Complete at least two more trials for the same angle of inclination. For each trial, take your two values of the slope and plug them into the formula: gsin(theta)=[(a1+a2)/2]. Doing this allows us to disregard the force of friction and isolate gravity as the only force affecting the acceleration of the ballistic cart.

7.      Repeat the experiment for a larger value of theta by either using a larger block of wood or upending the wood block you have (if materials allow) to elevate the aluminum track even further. Doing this assures that the angle of inclination increases.

8.      Print out copies of the two graphs from the trials in order to show the set of data from the position and velocity graphs. Show the time intervals used and the slope of the two different velocity curves on the graphs.

1.      What type of curve do you expect to see for x vs t and v vs t? Explain.

For the position curve (x vs t), a parabolic shape is the expected result because the ballistic car travels up the incline and then hits an apex at which point it descends again. Since the position function is parabolic in shape, then the velocity function must be represented by a linear function because the derivative of the position function is the velocity function.

trial 2

trial 1

trial 3

trial 5

trial 4

         

after we set up every thing we ran our trials where we let the car go down the ramp to the end of the ramp where after several trials we got  good values that gave us nice position vs time graphs and velocity vs time up above are some pictures of the trials we did they also shows how we solved them.using this formula
g sin θ  =
(a1 + a2) /2.

In this lab i was able to calculate how gravity affects object on an incline plane our percent difference we got from using the above equation was close that to 9.80m/s^2.also got to to some more work with the graphical analysis.

Working with Spreadsheets

purpose:To get familiar with electronic spreadsheets by using them in some simple applications.
equipment:Computer with EXCEL software.

procedures:
 Our instructor gave a quick introduction on how to use the program excel on a computer should us how to use the basic tools to work on a spreadsheet we where given the equation f(x) = A sin(Bx + C). we where instructed to set  up a spreadsheet and find the values of this equation.



part 1
       Their was values given also they where A = 5, B = 3 and  C = π/3shown on figure 1 shows a which is the amplitude,b the frequency, and c the phase.

fig 1


part 2
The next step on this lab  was to enter our values for x (radians) into the column D. There were 100 values of x to calculate, from 0 to 10 in intervals of 0.1 radians. This was done quite easily by entering our first two numbers (0 and 0.1), proceeding to use the copy feature in excel to create our table of values all the way to 10

then we plugged in the values in the function that was given to us in our instructions ( f(x) = A sin(Bx + C)). the lines where given $ for the constant before and after each column header so all our values would remain the same but the (x) values would change the 100 times.

from doing this spread sheet we where able to  obtained a table of x and y values for our function. In order to see how the function behaved, the table of x and y values were copied and pasted into the graphical analysis software. The curve fit was set to be the graph of a sin function, and the values of A, B, and C all matched the coefficients that were entered in this lab excel originally. The only difference was the rounding off of C (π/3).

 

in this lab we learned how to use excel to insert data or functions or gathering info and to do multiple calculations at once saving us some time . it be to much work to do all the work  by hand so that's what this lab helps us how to master excel so the next upcoming labs we know how to input our data and save our self some time.