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Acceleration down a slope

Introduction

In 1589, the experiment that Galileo have done on The Leaning Tower of Pisa which let two different objects with different mass fallen down to the ground free proved that acceleration is irrelevant to object's mass. (Baidu Baike, 2009)

According to Oenoki, acceleration is defined as the rate of the change of the speed. The unit of velocity is m/s, therefore, the acceleration is measured in (m/s)/s. Since velocity is a vector, the acceleration can also be positive or negative. (Oenoki, 2009)

According to the Student Worksheet, acceleration can be calculated. If an object slips down a slope by measuring the distance it moved and the time it used. The equation for uniform acceleration can be shown as:

s=ut+1/2a.

In this equation, s is the displacement, u is the initial velocity and t is the time used. When the initial velocity is zero, the equation can be transformed to:

s=1/2a

The aim of this experiment was to prove acceleration exists by using a slope and a object measure that the equation for uniformly acceleration is true. .

Method

The equipment that was used for this experiment includes a wooden board, a clamp stand, a meter-ruler, a stopwatch and a pellet. The length of the wooden board was measured; the board was set at an angle by the clamp stand which allowed the pellet would took at least two seconds to roll down the whole length.

Seven points were marked at different distances on the board from the top to the bottom. The lowest point was 0.8m from the start point and the distance between the points was 0.lm.

The time t taken for the pellet to roll from rest from the top of the board to each marked point was measured, the procedure was repeated three times.

Results

The results of the seven measurements are shown in Table A. Column 1 shows the distance between the marked points and the start point, Column 2 shows the first of the time that the pellet used to move through the seven marked points, Column 3 shows the second of the time that the pellet used to move through the seven marked points, Column 4 shows the third of the time that the pellet used to move through the seven marked points, Column 5 shows the average time of column 2 to column 4 and Column 6 shows the square of the average time.

Distance

Time 1

Time 2

Time 3

average Time

average Time

0.2m

0.70s

0.80s

0.80s

0.77s

0.59s

0.3m

1.00s

1.20s

1.20s

1.13s

1.28s

0.4m

1.40s

1.50s

1.40s

1.43s

2.04s

0.5m

1.50s

1.50s

1.50s

1.50s

2.25s

0.6m

1.60s

1.80s

1.75s

1.70s

2.89s

0.7m

1.70s

1.90s

1.85s

1.85s

3.42s

0.8m

2.00s

2.10s

2.00s

2.03s

4.12s

Table A. Length and time data from the experiment

Discussion

The results in the table A were shown in the diagram below

According to Jaywin(2006) errors can be divided into two different kinds, the approximation error and the absolute error. Approximation error is defined as the data is recorded in an approximate number because the accurate data can not be recorded, for example, commonly used as 3.14, and this can make the results have errors. Absolute error exists by the equipment in the experiment. (Jaywin, 2006) The plots in the diagram are not in a straight line, this is cause by absolute error, (Jaywin, 2006). Why the line is not linear due to three main reasons. The first reason is the air resistance, although the air resistance is nearly zero, but it does exist in the experiment. The second reason is the friction from the wooden board; it is the same as the air resistance. The third reason is the error from the stopwatch. Since the stopwatch was controlled by human, the time result is inaccurate. After the time was squared, the error can be more serious. To improve the accuration of the results of the experiment, the following solutions can be used. The first solution is to use an air track instead of the wooden board, which can decrease the friction and make the results more accurate. The second solution to is use an electrical stopwatch or let two or more persons recording the data at the same time to reduce the time error, which is the significant error from the experiment.

Conclusion

From Table A, the numerical value of acceleration in the experiment is approximately 0.36(m/s)/s, The equation of linear regression in the diagram shows that the acceleration is constant, which proves that when the kind of motion of the object is uniformly variable motion, the equation for uniformly acceleration can be proved was true.

REFERENCE

Oenoki, K (2006) [online] Acceleration Available at:

http://library.thinkquest.org/10796/ch3/ch3.htm (Accessed 07/1997)

Jaywin (2006) [online] Approximation Error available at http://psychology.wikia.com/wiki/Approximation_error (Accessed 29/12/2006)