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