acceleration=

However, from the derivation of the formula of acceleration down the slope of an inclined plane, it can be written that

acceleration=g ⋅

The inclined plane was constructed of two meter sticks (joined together at right angles such that the ball could descend the slope), adjustable metal bars (used to set the height of the plane, and the corresponding magnitude of the angle (θ)). The plane was set up on a lab table, where the top of the table was the horizontal to the incline. A small rubber ball was used to measure the acceleration due to gravity (of the angle (θ)). The time that it took for the ball to roll down the slope was measured by the experimenter. In order to have the most accuracy, the ball was released and timed by the experimenter, to eliminate human error. The ball was times with the timer on a TI-84®

For the most accurate measurements of the acceleration due to gravity at angle (θ), the ball was rolled down the ramp at three inclines of θ = 10˚, 15˚, 30˚ five times each. The elevation was set by the heightening and lowering of the incline.

The acceleration was calculated by using the formula

vfinal - vinitial/ time = acceleration

## Data Collection and Processing

Time Trials

Trial Analysis

## Calculations

= = = 0.173

sin-1(17.3) = 10˚

velocity (average) = = ms-1

Velocityfinal = (acceleration)(time)

a = = = 0.898 ms-2

= = = 0.258

sin-1(25.8) = 15˚

velocity (average) = = ms-1

Velocityfinal = (acceleration)(time)

a = = = 1.49 ms-2

= = = 0.5

sin-1(0.5) = 30˚

velocity (average) = = ms-1

Velocityfinal = (acceleration)(time)

a = = = 3.7 ms-2

## Analysis

The acceleration (in ms-2) was plotted versus (in radians)

## Rolling Acceleration

The relationship appears to almost be a straight line with slope of 8.69.

## Conclusion

In conclusion, the slope of the plotted line for the graph is not that of the acceleration due to gravity (9.8ms-2) at the surface of the earth. Human error can be attributed to the deviation from the true acceleration due to gravity. Some methods that could have been employed to eliminate some errors in order to have more accurate data may be to have more trials at more angles. Perhaps the measurement of only three different angles was inadequate to plot the linear regression line such that the data would show the acceleration due to gravity equivalent to 9.8n ms-2. Another improvement could have been to have an automatic timer to eliminate human error with respect to the time trials. The timing of the ball rolling down the ramp is subjective to some degree, though it is timed with a timer, it is subjective to some degree, as the student doing the timing decides when to stop and start. A longer ramp may have improved the time trials, as the time interval to measure steeper angles would not have been so small. A smoother ball such as a bowling ball (on a much larger apparatus), or a billiard ball would have been more effective as some of the frictional force would have been reduced. Lastly, the inclusion of measurements of uncertainty would have helped as it would have been easier to assume whether or not the inaccurate results were acceptable.