In this lab, position vs. time data points will be taken of a cart moving up and down an incline. The motions of the cart traveling up, then down the incline will be treated as separate, then compared. Because the force of friction acts with the motion of the cart on the way up ramp, and acts against the motion on the way down the ramp, the average of the two accelerations will be taken with the following ratio:
gsin(A)=
(a1+a2)/2
where g= gravity, A= angle of incline, a1= acceleration up incline, and a2= acceleration down incline
Purpose:
The purpose of Acceleration of Gravity on an Inclined Plane 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.
Setup:
Tools used included the logger pro software, a motion detector, aluminum track, ballistic cart, carpenter level, meter stick, and a wooden block. The aluminum track was setup at an incline with the wooden block, and then carefully leveled. We then measured the change in height of the two sides, to the horizontal length of the inclined ramp (pictured in fig 1). The angle of the ramp was then calculated with the following ratio:
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| fig 1 |
A=angle of incline on ramp
Tan-1((y2-y1)/(x2-x1))=A
Tan-1((12.9cm-6.7cm)/(228.2cm))=A
A=1.56o
Procedure:
After the setup was completed, the trial runs were performed where the cart was tossed up the ramp and then fell back down. It took a few practice runs in order to obtain a trajectory that did not come within 50 cm of the motion detector. Three trial runs were completed first for the inclination angle of 1.56 degrees, and then the process was repeated for an inclination angle of 3.6 degrees.
What type of curve do you expect to see for x vs. t and v vs. t? I expect that the curve of x vs. t would be a parabola with the left side having a more rapid change in slope than the right because of friction acting with motion of the cart on the way up and against it on the way down. I also expect the graph of v vs. t to be linear with different slopes on the motion up and down the ramp (because of the effect of friction that changes the acceleration).
Shown below are the position vs. time and velocity vs. time graphs of our first trial at an angle of 1.56 degrees.
After the setup was completed, the trial runs were performed where the cart was tossed up the ramp and then fell back down. It took a few practice runs in order to obtain a trajectory that did not come within 50 cm of the motion detector. Three trial runs were completed first for the inclination angle of 1.56 degrees, and then the process was repeated for an inclination angle of 3.6 degrees.
What type of curve do you expect to see for x vs. t and v vs. t? I expect that the curve of x vs. t would be a parabola with the left side having a more rapid change in slope than the right because of friction acting with motion of the cart on the way up and against it on the way down. I also expect the graph of v vs. t to be linear with different slopes on the motion up and down the ramp (because of the effect of friction that changes the acceleration).
Shown below are the position vs. time and velocity vs. time graphs of our first trial at an angle of 1.56 degrees.
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| fig 3 position vs time graph |
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| fig 4 velocity vs time |
Position vs. time graph
Velocity vs time graph, note how the motion on the way up the ramp has a greater change in velocity than the motion down the ramp due to friction
In order to obtain our values for a1 and a2, a linear fit was applied to the negative velocity portion of the v vs. t graph for a1, as well as a linear fit to the positive velocity of the v vs. t graph for a2. The slope from our linear equation then became our separate accelerations
Data:
Our data for each of the trial runs is shown in the spreadsheet. The first table is for a ramp angle of 1.56 degrees, and the second for an angle of 3.6 degrees. a1 is the cart's acceleration up the inclined ramp, and a2 is the cart's acceleration down the track.
Conclusion:
Once the data had been collected, verification of our numbers compared to the accepted value of acceleration due to gravity was needed. Since the force of friction acts with the force of gravity on the way up the ramp and against it on the way down, the average of the two accelerations will be taken to equate our experimental value of acceleration due to gravity. The formula used to calculate Gexp was:
Gexpsin(1.56)=(a1+a2)/2
-Trial one of 1.56 degree incline
Gexpsin(1.56)=(0.33
m/s2+0.18 m/s2)/2
Gexp=9.4m/s2
In this lab the group was able to determine with reasonably close accuracy the effect gravity has on objects that are on inclined planes. The percentage differences they calculated in this lab seemed to match well with the accepted 9.8 m/s2. The most inconsistent value was 9.4 m/s2 at a 4.1% difference. Potential sources of error in this lab would have included various factors such as the friction between the car and the track, and performing the linear fit to the velocity vs. time graphs in different domains.
Nice writeup Marcus. grade == s
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