The lab demonstrates what kind of motion is observed when the metal trolley is let freely down the inclined plane.
MOTION OF THE TROLLEY
ON INCLINED PLANE
Aim: The lab demonstrates what kind of motion is observed when the metal trolley is let freely down the inclined plane.
Hypothesis:
If the metal trolley is let free down the inclined plane, its move will be accelerated. Later, as the air resistance and friction force have influence on acceleration, they will change it.
Analysis:
The first part of experiment included preparing an inclined plane. The physics book by Giancoli was laying down on one table, while the other school table was laid on the book. This action is presented on the Drawing 1. The length of the school table is 120±1 cm measured by a ruler. The width of the table is not required. The difference in levels between a table and the highest point of the inclined plane is 6.8±1 cm .
Using a ruler with exactness to millimeters and a chalk, we calculated and determined six distances of the same value 15 cm with the uncertainty of 1 cm. Next we checked if the stopwatch worked properly and checked the trolley. Its size is 19±1 cm; its mass is not relevant.
The most important part of the experiment included precise measurements. In order to do that, we repeated measurements of distance and time the trolley needed to travel given distance. Each measurement took place 10 times. Six distances measured ten times gave a total amount of sixty measurements. Using 10 measurements we calculate the average time taken to travel given distance. We added all ten measurements of time for each distance and divided by ten. The results can be seen in the Table 1.
Then, the equation V=d/t was used. The velocity was calculated and so was the change of time and the change of velocity. Then all results were recorded in Table 3 Later on, a=?V/?t was used. The acceleration for each time was calculated and recorded in Table 3. Another step was to calculate the uncertainty of the acceleration using the equation: ?a/a= ?v/v+?t/t. The time, the velocity and the acceleration from the Table 3 were used and the results were recorded in Table 3. The uncertainty of the distance is 1 centimeter and is constant; the uncertainty of time is 0.05 second and also is constant. The uncertainty of velocity and acceleration is not constant.
After recording all necessary datas, the averages of time, velocity, acceleration and uncertainty were calculated- the measurements of each six distances were added and divided by number of the measurements-six. All measurements were rounded to second decimal place.
The next step to measure the acceleration was constructing the graph showing the distance dependence on time (Graph 1). The best-fit line was drawn, so were the line of maximal slope and the line of minimal slope. Then, the Graph 2 showing the average acceleration dependence on time was constructed. The best fit line was drawn. Last step was ...
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After recording all necessary datas, the averages of time, velocity, acceleration and uncertainty were calculated- the measurements of each six distances were added and divided by number of the measurements-six. All measurements were rounded to second decimal place.
The next step to measure the acceleration was constructing the graph showing the distance dependence on time (Graph 1). The best-fit line was drawn, so were the line of maximal slope and the line of minimal slope. Then, the Graph 2 showing the average acceleration dependence on time was constructed. The best fit line was drawn. Last step was creating a Graph 3 representing the relationship between given velocities. velocity
In the experiment, the values of air resistance and friction force were neglected, but the air resistance and friction force has influenced the whole experiment.
Drawing 1: the incline plane
h-height of the school table
l-length of the school table
TABLE 1: Measurements of time in seconds.
First t ±0.05s
Second t ±0.05s
Third t ±0.05s
Fourth t ±0.05s
Fifth t ±0.05s
Sixth t ±0.05s
0.62 s
0.87 s
.27 s
.53 s
.77 s
2.02 s
2
0.65 s
0.99 s
.25 s
.52 s
.81 s
.99 s
3
0.58 s
.02 s
.25 s
.57 s
.82 s
2.04 s
4
0.62 s
0.87 s
.22 s
.50 s
.77 s
2.05 s
5
0.65 s
0.98 s
.26 s
.55 s
.80 s
2.04 s
6
0.57 s
0.93 s
.27 s
.50 s
.71 s
2.05 s
7
0.63 s
0.99 s
.26 s
.56 s
.77 s
2.00 s
8
0.59 s
0.98 s
.28 s
.58 s
.79 s
2.03 s
9
0.65 s
0.96 s
.27 s
.51 s
.80 s
.98 s
0
0.62 s
0.95 s
.30 s
.52 s
.73 s
2.03 s
Average:
0.62 s
0.96 s
.26 s
.53 s
.78 s
2.02 s
Rounded to 2 decimal place
Uncertainty results from the inaccuracy of the timer.
TABLE 2: Measurements of distance, time and its change.
d [cm] ±1.00 cm
t [s] ±0.05 s
?t[s]=ty-tx ±0.05 s
5.00
0.62
0.62
2
30.00
0.96
0.34
3
45.00
.26
0.30
4
60.00
.53
0.27
5
75.00
.78
0.25
6
90.00
2.02
0.24
Rounded to 2 decimal place
TABLE 3: Time, velocity, acceleration and uncertainty.
?t[s]
v [cms-1]
a[cms-2]= ?v/ ?t
?a [cms-2]
0.62±0.05
24.19
39.02
.00
2
0.34±0.05
44.12
58.60
0.60
3
0.30±0.05
50.00
9.61
0.30
4
0.27±0.05
55.56
20.58
0.30
5
0.25±0.05
60.00
7.78
0.30
6
0.24±0.05
62.50
0.42
0.20
Rounded to 2 decimal place
?a=(amax-amin)/2 ?v =(Vmax-Vmin)/2
?a=(58.60-10.24)/2 ?v=(62.50-24.19)/2
?a=24.18 ?v=19.55
Graph 1: The graph represents the displacement dependence on time during the trolley movement. Best-fit Line, maximal and minimal slope are drawn.
Graph 2: The graph present the best-fit line of average acceleration dependence on time during the trolley movement..
Graph 3: The graph presents the best-fit linr of time dependence on velocity during the trolley movement. The velocity increases in each second of the movement.
Graph 4: The graph present the best-fit line of acceleration dependence on time. It can be seen that the acceleration decreases with time, which is the result of the activity of friction force and air resistance.
Conclusion:
The constructed graphs doesn't support the hypothesis. The line touches all error bars, so it means there is a relationship between the linear quantities. The unit of the uncertainty of the distance is expressed in centimeters, the uncertainty of time in seconds and the uncertainty of acceleration in centimeters per second square. The air force and friction has a significant influence on the value of acceleration during the experiment. The conclusions are reasonable. The graph 1 and 3 indicates that there is displacement and velocity, not equal to zero or to negative value, which means that the body is moving- it's the confirmation that the trolley on the inclined plane is -in fact- moving. What is more, graph 4 confims my hypothesis, that the air resistance and friction force change the acceleration. It means that acceleration rather than increase, in this case-decreases.
In the experiment there was error due to the lack of precision of the ruler. It's not possible to be precise using the standard ruler measuring with precision to millimeters. Another possible error can be present due to the inability to see and mark the exact point where the identical distances were. Error also came from inability to know exactly when to stop the timer; also the additional seconds-reaction time of the experimentator. Human reaction for using the timer is 0.15 s for each turning on and off, so it gives 0.30 s for both. Given errors could cause further errors in calculations of accelerations. All errors have reasonable values. The values of the measurements are similar to each other. The number of repetition is proper. The error also occurred because of the paralaxa effect. Because the eyes of humans are in different positions on the head, they present different views simultaneously.
The fact that the graph doesn't go through the point (0,0) shows presence of the systematic error. As the exact value of air resistance and friction forces were not regarded, the error could occur. There also could be the error due to the slight change of levels because of soft cover of Giancoli.
As all experiments, this one also involve errors and can be improved. The uncertainty could be reduced, the millimeter paper could be used instead of the ruler, hard cover instead of Giancoli. Considering air resistance and friction force could help with estimating particulars. The usage of more precise timer could also improve our measurements and further analysis. More readings could give better results and therefore improve the whole experiment. The fact that the inclined plane had a high angle could also change the expected results; if the inclined plane was lower, the results would be more precise because the trolley would move slower, so it would be easier for a human to measure time-the uncentainty of time would be lower. To avoid parallax error, we should take measurements with our eye on a line directly perpendicular to the ruler, so that the thickness of the ruler does not create error in positioning for fine measurements.
Not including and using in calculations the values of air resistance and friction force has influenced the calculation, and what follows, the results of the experiment. If the values of air resistance, fraction force and other variables were considered and therefore calculated, it would show, that our experiment was done correctly.
Gracja Kowalska kl.II ib 2008-10-22