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.

vector addition of forces

Purpose:

To study vector addition by:

1) Graphical means and by

2) Using components.

A circular force table is used to check results.

Equipment:

Circular force table, masses, mass holders, string, protractor, four pulleys.

circular force table / four pulleys

protractor

Procedure:

1. Your instructor will give each group three masses in grams (which will

represent the magnitude of three forces) and three angles. Choose a scale of

1 cm = 20 grams, make a vector diagram showing these forces, and

graphically find their resultant. Determine the magnitude (length) and

direction (angle) of the resultant force using a ruler and protractor.

2. Make a second vector diagram and show the same three forces again. Find

the resultant vector again, this time by components. Show the components of

each vector as well as the resultant vector on your diagram. Draw the force

(vector) you would need to exactly cancel out this resultant.

3. Mount three pulleys on the edge of your force table at the angles given

above. Attach strings to the center ring so that they each run over the pulley

and attach to a mass holder as shown in the figure below. Hang the

appropriate masses (numerically equal to the forces in grams) on each string.

Is the ring in equilibrium? Set up a fourth pulley and mass holder at 180

degrees opposite from the angle you calculated for the resultant of the first

three vectors. Record all mass and angles. If you now place a mass on this

fourth holder equal to the magnitude of the resultant, what happens? Ask

your instructor to check your results before going on.

figure 1

figure 3

figure 2

figure 4

Vector Calculations:
Rx = (100Cos(0)) + (200Cos(71)) + (160Cos(144)) = 36.1
Ry = (100Sin(0))  + (200Sin(71))  + (160Sin(144))  = 283
ø = 82.7°              R = sqrt(283^2 + 36.1^2) = 285.3  



The simulation confirmed the results as correct. *Note: scale to 1=10.

The diagram shows vectors A, B, C and D as the sum. (1 cm = 20 g)

figure 8

conclusion:during our lab experiment we learned that in order to get three forces that where given. to be in equilibrium a forth force would be necessary to counter- balance the other three forces this force would have to be negative and would be the sum of all 3 forces.

lab2

purpose:

1To determine the acceleration of gravity for a freely falling object         

2 To gain experience using the computer as a data collector.

equipment:



 

logger pro

motion detector

•  wire basket
• rubber ball

Introduction:

         In this lab we use the computer to collect some position(x)vs. time (t)data for a rubber ball being tossed in to the air > since the velocity of an object is equal to the slope of the x vs. t curve, the computer can also construct the graph of v vs. t by calculating the slope of x vs. t at each point in time.We  will use the both the x vs. t graph and the v vs. t graph to find the free fall acceleration of the ball.

procedures:1.  Connect the lab pro to computer and motion detector to DIG/SONIC2 port on lab pro. Turn on the

computer and load the Logger Pro software by double clicking on its icon located within the Physics

Apps folder. A file named graph lab will be used to set up the computer for collecting the data

needed for this experiment.  To open this file, first select File/Open and then open the mechanics

folder. When this folder opens, open the graph lab file.

2.  You should see a blank position vs. time graph.  The vertical scale (position axis) should be

from 0 to 4 m while the horizontal scale (time axis) should be from 0 to 4 s.  These values can be

changed if you desire by pointing the mouse at the upper and lower limits on either scale and

clicking on the number to be changed.  Enter in the desired numbers and push the Enter key.

3.  Place the motion detector on the floor facing upward and place the wire basket (inverted) over

the detector for protection from the falling ball.  Check to see that the motion detector is

working properly by holding the rubber ball about 1 m above the detector.  Have your lab partner

click on Collect button to begin taking data and then move your hand up and down a few times and

verify that the graph of the motion is consistent with the actual motion of your hand.  After 4s

the computer will stop taking data and will be ready for another trial.  If your equipment does not

seem to be working properly ask for help.

4.  Give the ball a gentle toss straight up from a point about 1 meter above the detector.  The

ball should rise 1 or 2 m above where your hand released the ball.  Ideally your toss should result

in the ball going straight up and down directly above the detector.  It will take a few tries to

perfect your toss.  Be aware of what your hands are doing after the toss as they may interfere with

the path of the ultrasonic waves as they travel from the detector to the ball and back.  Take your

time and practice until you can get a position-time graph that has a nice parabolic shape.  Why

should it be a parabola?

5. Select the data in the interval that corresponds to the ball in free fall by clicking and

dragging the mouse across the parabolic portion of the graph.  Release the mouse button at the end

of this data range.  Any later data analysis done by the program will use only the data from this

range.  Choose Analyze/Curve Fit from the menu at the top of the window.  Choose a t^2+ b t + c

(Quadratic) and let the computer

find the values of a, b, and c that best fit the data.  If the fitted curve matches the data curve,

select Try Fit.  Click on OK if the fit looks good.  A box should appear on the graph that contains

the values of a, b, and c.  Give a physical interpretation and the proper units for each of these

quantities (Hint: use unit analysis).  Find the acceleration, gexp, of the ball from this data and

calculate the percent difference

between this value and the accepted value, gacc, (9.80 m/s2).

6. Look at a graph of velocity vs time for this motion by double clicking on the y-axis label and

select “velocity” and deselect “position”.  Examine this graph carefully.  Explain (relate them to

the actual motion of the ball) the regions where the velocity is negative, positive, and where it

reaches zero.  Why does the curve have a negative slope?  What does the slope of this graph

represent?  Determine the slope from a linear curve fit to the data.  Find the values of m and b

that best fit the data. Give a physical interpretation and the proper units for each of these

quantities (Hint: use unit analysis). Find the acceleration of the ball, gexp, from this data and

calculate the percent difference between this value and the accepted value, gacc. Put together an

excel spreadsheet for your data like the one shown below. Finally, select Experiment/Store Latest

Run to prepare for the next trial.

7.  Repeat steps 4 - 6 for at least five more trials.  Obtain an average value for the acceleration

of gravity and a percent difference between this value and the accepted value.

  

Results:


table

  

trial 1



trial 2



trial 3



trial 4

trial 5

conclusion: This lab gave us a clear understanding of object being thrown in the air gave us more practice on using the software logger pro and using motion detector to detect the data of our ball when we through it up in the air. from our results we where able to find the slope for each trial.most of our trials where near our gravitation force our percent error was about -1.2% difference.

lab1

the purpose of  the lab was to gain experience in drawing graphs and using graphing software. we also learned how to use the motion detector to determine the velocity and acceleration of a dropping ball.


the materials we used for this lab:

• graphical analysis software
• lab pro interface
• logger pro software
• motion detector
• rubber ball
• wire basket

Part 1
On this part of the lab we used the software graphical analysis software we where given instructions to open a file where a previous graph with its table and data which had 3 different values in x1,x2,x3 still same graph just different ranges. this information was given to us so we could create our own function and get a graph and create our own values and give it a tittle label the x, and y axis and label units.

The equation we created was F(x)=(x2)^5sin(3x2).

we used this graph to illustrate a heart beat do to its sin waves at each end running from -0.5<x>.05

Part 2

on this section of the lab we set up a motion detector on the floor being covered by a basket we where instructed to drop a ball above the motion detector. which was plugged to the logger pro software to record the fall of the ball.which gave us a graph

the data we collected from this graph gave us how long it took for the ball to hit the ground . the we proceeded to to a curve fit on the graph which then we determined it was a quadratic function which was -7.175t^2+10.56t-2.067
                                                        unit analysis
to find the distance at a certain time you could use the equation d=gt^n where d is the distance (m), g is gravity (m/s^2), and t is time (s). To find what n would be we do the following unit analysis:


                                                       d=gt^n
                                                      m=(m/s^2)s^n
                                                      ms^2=ms^n
                                                      n=2



conclusion
in this lab we got to work together built our team work skills got to used some interesting software the logger pro motion detector  and graphical analysis. with all these programs we where able to create graphs using live data.