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# The acceleration of an object down a slope

### Introduction

A car can take 3 seconds to accelerate to 20m/s from rest and it also can reached the same velocity in 30 seconds from rest. It said that the car could reach from the same initial velocity with using different time. However, the velocity of the car which using less time changes faster than the other. The quantity for describe how quickly did the velocity change is acceleration. In other words, "acceleration is the rate of change of velocity." (Duncan, 2000)

While an object rolls down a slope, the mass and the resultant force of the object can be seen as constant. Therefore, according to Newton's second law, the acceleration of this object is uniform, which gives:

On account of the resultant force and the mass were constant, the acceleration is uniform.

According to Duncan (2000), assume the velocity of an object changes from u to v constantly in time t and the distance is s, the uniform acceleration a is given by

If the object is moving from rest, in other words, the initial velocity is zero, it is easy to know that and it is easy to find out any one of the quantities in the equation of an object moving from rest if any two quantities are known.

The aim of the research was to find out the acceleration of a short metal roller which rolled down a slope.

### Method

The instruments used for measuring the acceleration a of the short metal roller rolling down the slope consisted of a clamp stand, a clamp regular holder, a thin steel stick, a plank with a hole in the side, and a graduation in the other side and a dam board in the end, a metal roller, a stop watch and a metrestick. The sketch of the instrument is shown above in Figure1.

The experiment processes are showed below:

First, the length of the plank was measured with the meter stick (0.85m).

Second, the six distances that the roller rolled down were defined (0.80m, 0.75m, 0.70m, 0.60m, 0.50m, 0.40m).

Third, the start lines were drawn with a pencil on the plank according to the second step.

Fourth, the plank was set up with the clamp stand and it was at an angle with the horizontal.

Fifth, the roller was laid down on the top of the plank, and released from rest.

Sixth, the time of the roller from being released to colliding with the dam board was measured by the stopwatch.

Seventh, the angle between the plank and the horizontal was changed until the time measured in the fifth step is equal or less than two seconds.

Eighth, the time of the roller downing the slope that released at start line from the rest was measured with the stopwatch.

Ninth, the process of the eighth step was repeated six times.

Tenth, the start line was changed.

Eleventh, the processes of step eight, nine, and ten were repeated in turn until all the start lines were used.

### Results

 D(m) T1 (s) T2 (s) T3(s) t4 (s) t5 (s) 0.80 2.20 2.17 2.21 2.19 2.18 2.190 4.796 0.75 2.17 2.14 2.12 2.16 2.14 2.146 4.605 0.70 2.02 2.02 2.05 2.05 2.01 2.030 4.121 0.60 1.86 1.86 1.87 1.88 1.84 1.862 3.467 0.50 1.65 1.61 1.65 1.66 1.60 1.634 2.670 0.40 1.50 1.51 1.48 1.49 1.49 1.494 2.232

The results of the six measurements are showed in Table 1. Column 1 shows the distances of the roller travelling and the unite is metre. Columns 2 to 6 show the time of the roller used in different distance in seconds. Column 7 shows the average time of each distance in seconds. Column 8 shows the average time squared, the unit is second squared.

### Discussion

According to in the theory, it is easy to know that. However, the time of the same distance were different, therefore, the values of the acceleration calculating by different data may be different with each other. Some of them may larger than then real value and some of them may smaller than the real value. Hence, calculate the average value of the acceleration each distance and then use the values to calculate the average acceleration which may be more near the value of the acceleration. The acceleration of each distance can be calculated from, the average acceleration

Table 2 shows the value of acceleration of each distance and the average acceleration value.

 D(m) a(ms-2) (ms-2) 0.80 0.3336 0.75 0.3257 0.70 0.3397 0.3463 0.60 0.3461 0.50 0.3745 0.40 0.3584

There are some reasons for creating errors. The distances were measured by human, but eyes can not read the graduation accurately, therefore, there were some errors in the distances. The roller may not rolled in a straight line if it's sides were not parallel with the edge of the plank then the traction that the roller got was changed, the acceleration was changed. It is also difficult to know whether the side of the roller is parallel with the side of the plank and whether the plank has a line in it parallel both the edge of the plank and the horizontal. The most serious errors is from the measurement of the time. It is almost impossible for human to release the roller and start measure the time by using the stopwatch at the same time. It is also impossible for human to stop the watch when the roller collide the dam board. Add the errors on the degree reading, it will make a great error.

After knowing the reasons about the production of errors, it is necessary to find out how to reduce them. For the errors of the time, it can be more accurate if measure a large mount of data and calculate their average value., The errors of the length can reduce by different people measuring the length, and finding out the average length they got. To reduce the errors from the experimental facility, a globule and a notch can be used to instead of the plank and roller. The instrument is shown in Figure 3.

### Conclusion

The acceleration of the roller has been got in the experiment by using a roller and a slope which set up by a plank. The value can be improved by measuring large amount of data and calculating the average value and using a globule and notch to replace the plank and roller. Measuring the data with the electric equipment may improve accuracy.

### REFERENCE

Ducan, T (2000). Advanced Physics (5th Edition). London: John. Marray Publishers