Acceleration of Gravity on an Inclined Plane

Acceleration of   g  on an Inclined

Purpose:  To find the acceleration of gravity by studying the motion of a cart on 
             an  incline  as well as gaining further experience using the computer for data collection 
        and analysis. 

Equipment: Windows based computer with Logger Pro software, motion detector, ballistic cart, aluminum track, wood blocks, meterstick, small carpenter level.
     
         Introduction:

In this lab we toke a cart and roled it up an incline then watched it come back down.  With our computers we collected data of the cart accelerating on the track as it went up and came down looking at the position vs time graph.  Since we were rolling the cart up the incline and then it would role back down the effect of friction was eliminated leaving the effect of gravity only.  We said that if g was the accceleration of gravity when an object was at free fall, the   relationship of the objects acceleration along the track is g sin O having theta be the angle of incline for the track.    









        So we got some measurements
 and began to look for our angle
of incline using the formula
  
     Tan o =delta y/ delta x. 

Our first angle
of incline came out to 1.56 degrees.  When our data collector begins to graph our data we expect to see a X vs T graph that looks like a parabola.  Since the motion detector was placed at the top of the rail, @ the time the cart reaches the top it would be as if its getting closer to zero.  Then the cart will head back down getting further away from zero.  For our V vs T graph we expect to see a graph that starts at a negative position with velocity decreasing moving towards zero in the positive direction.  Then continue in the positive direction but after it crosses zero increasing in velocity.  We began testing comparing both X vs T and v vs t graphs.  The graphs revield smooth consistent curves so we knew we were in the right path. For the r vs t we got a graph that showed a parabola that was going in a negative dirrection then it flatend out and started going up into the positive dirrection.  It was exactly what we expected.  Our V vs T graph disclosed a graph similar to the one we were expecting.  This makes sence because the object is being pushed up in a positive dirrection but gravity is pulling on it so the acceleration is negative and oposite to the velocity slowing the object down and decreasing the velocity.  When it runs out of juice it hits 0 velocity and begins to come back down in the same dirrection as the acceleration vector giving it an increasing velocity.


 On the v vs t graph we were able to see that our graph started out at a negative position decreasing until reaching zero then crossing over to the positive derection and increasing in value untill it hits the bottom. By determining the slopes of the v vs t curve we were able to find the accelerations a1 & a2 (up/ down)  We did this easaly by choosing analyze/curve fit. Both the computer and our technique of

g sin O= a1-a2/2 
                               showed us the results for g.

  After averaging our values for g and comparing them to the accepted value of 9.8 m/s 2  we flipped the wood block up so it would give us a greater angle.  We repeated the experiment and came to find out that our juristiction of error got closer to the g accepted value of 9.8 m/s 2 with a larger incline.          

 Conclusion:           Since we are mesuring in meters and that measuring system is a bigger unit system, when dealing with small angles the measurings seem to be more unacurate.

 

       Error:     In  this experiment we need to consider source of error.  Some source of error came from the measurements we toke in tring to figure out our angle of incline.  Other error could have came from the table not being leveled.  One error that we know for a fact is the % error we had to calculate  

 

                        % error = Exp g  -  actual g  x 100 / actually g

 

 

Graphical Analysis 8/21/12

On todays lab we got to play around in the computer with a physics app called Graphical Analysis.  It consists of three main windows; text, data table, and graph.  We explored all three of them and then went on to opening a file that had been prepared for this lab.  It showed a graph of a function and the data used to create the graph.  We then entered our own function and it gave us a graph.  We created a title for it (Algie Bacteria) and labeled days for the y axis.  Then used anount of bacteria for x axis and played around with our units untill we were satisfied with the given graph. 






After we had completed our graphs and were comfurtable with the system we were asked to connect our lab pro (a machine used to measure motion) to the computer and load the logger Pro software. We then used a board to record positon vs. time graphs.  After a few trials we used a ball to measure free fall.  We gently tossed the ball up into the air and watched it fall while the logger pro recorded.  We had trouble at first getting a nice curve due to one of the bars from the protecting basket running through the middle of our lab pro.  Once removed we were able to get a nice curve.  We then preform a fit to the data and got a free fall of 4.894 which is around half the 9.8 amount assigned to free fall. 

Acceleration of Gravity

Acceleration of Gravity

The purpose of this lab was to determine the acceleration of gravity for a freely falling object.  In our previous lab we played around with the computer using it as a data collector so our experience this second time around was a lot more rewarding. 

The equipment used were the same as last lab: Windows based computer, Lab Pro interface, Logger Pro software, motion detector, rubber ball, and a wire basket.

We began by connecting the lab pro to the computer  and the DIG/SONIC2 port to the lab pro.  We loaded the logger pro software to the computer this is found within the Physics Apps Folder and Opened the mechanics folder. Once inside the folder we open the graphlab file which is used to set up the computer for collecting data. Once we opened our folder and got a blank r vs t graph we place the motion detector on the floor and the basket over it to protect it.  We checked that it was working properly by testing the data colletion with a piece of carboard.  Everything seem to be working fine so we began to Collect data.  We tossed the ball stright up and watched the computer collect data.

 

 After adjusting our time on the x axis to 4 seconds and a couple of tries a nice parabolic curve appeared on our position vs time graph.  The graph showed a steady line that was probably when we were holding the ball.  Then it goes up with the toss and it heads back down pass the initial stating point. We then choose the Analyze/Curve Fit from the menu and put     a t^2+b t+ c (Quadratic equation form).  We selected the points from 1s to 2s the selected try fit.  A curve almost identical to ours appeared . After pressing ok it gave us a box with the values of a, b and c.  Based on Unit Analysis 2A gives us our acceleration Gexp, we toke this value and pluged it in to the formula for calculating error percentage.
     










percent error= measured -actual / actual  x100%



 Then we double clicked on the y-axis and selected velocity and deselected position.  The velocity graph appeared.  The graph shows a velocity thats moving in a positive direction and slowing down that was when the ball was tossed up, then it hits 0 at the peak of the curve before turning back in a negative dirrection and speeding up in velocity this was when the ball ran our of juice and begun to head back down towards the ground.  It continued to go pass the starting point thats because the ball was released from a meter above ground.  In the same manner as the r vs t graph we measured the % error.  We did this 5 times got and average value rand the percent error calculation. 
On our black boards we sketched up all three graphs. r vs t  a vs t  and a motion graph.  In the motion graph which is the graph in the bottom you can see that the motion is moving in a positive direction and then it turns around and goes in a negative direction.  This should help explain acceleration having a positive and then a negative slop. The slop is positive decreasing and the it turns around negative increasing.