Ball+on+Incline-+Nathan+Devan,+Yuki+Kurosu,+Sanjana

Ball on Incline
 * Title of Lab: **

Nathan Devan Yuki Kurosu Sanjana Sreenath
 * Researchers: **

How does the time it takes for a tennis ball to roll down an incline relate to the that it travels?
 * Research Question: **


 * Research: **

ball on incline diagram source: [] x= v1(t) + 1/2 at^2 (where x= distance, v1= initial velocity, a= acceleration, t= time) - Kinematic equation v1=0 x= 1/2 at^2 [2(x)]/[a] = t^2

A ball free-falling would have an acceleration of 9.81m/s^2, but the ball in the experiment is on an incline which lengthens the time the ball takes to reach the bottom. The percent of reduction in acceleration (by the normal force) can be found with the equation (sin(theta))9.81m/s^2 where theta is the angle of incline. theta = 15 degrees.With this new rate of acceleration, we can use kinematics to mathematically find the relationship between the distance the ball travels and the change in time. sin(theta) times g = 2.54m/s^2 V1 = 0 Vf = x = 1, 0.8, 0.6, 0.4, 0.2, 0.1 m t = 1.2, 0.99, 0.86, 0.80, 0.66, 0.46 sec a=2.54m/s^2

**Hypothesis**: The distance the ball travels and the time taken to roll down are square relations such that [2(x)]/[a] = t^2 or 0.788x = t^2

**Procedure**: materials: ( plank, tennis ball, protractor, stopwatch, and meter stick)
 * 1) lean the plank on a surface perpendicular to the ground
 * 2) Using the protractor, measure the angle of inclination
 * 3)  Use the meter stick to measure a distance from the bottom (in meters) and r ecord the measured length
 * 4) Place the tennis ball at the desired distance
 * 5) Use a stopwatch and record the time it took for the ball to roll down the incline
 * 6) Record the time in seconds are repeat steps 3-5 two more times before changing the distance to a different point.

Data: chart of experimental measures from a 15 degrees incline
 * Distance (m) || Time 1 (s) || Time 2 (s) || Time 3 (s) || Time 4 (s) || Average Time (s) ||
 * 1.0 || 1.3 || 1.4 || .97 || 1.0 || 1.2 ||
 * 0.80 || .95 || 1.0 || 1.0 || 1.0 || .99 ||
 * 0.60 || .88 || .81 || .88 || .88 || .86 ||
 * 0.40 || .82 || .87 || .75 || .75 || .80 ||
 * 0.20 || .66 || .67 || .65 || . 66 || .66 ||
 * 0.10 || .45 || .45 || .49 || .46 || .46 ||


 * Data Analysis: **



slope:1.1 if the angle of the incline was greater, the slope of the graph would be smaller, if the angle of incline was smaller, the slope of the graph would be greater. This is because at a greater incline the ball travels faster and takes less time creating a smaller rise over the same run on the graph, thus a smaller slope. The slope was calculated by finding the change between two points on the line of best fit. This could be used to find the acceleration of a ball rolling down an incline. g= 2/(slope*sin θ), we find the experimental g is equal to 2/(1.1*sin 15)= 7.02 m/s^2. accepted g value: 9.81m/s^2 Y intercept, t, is 0 when d=0 m percent error: (9.81-7.02)/9.81= 28.4% source of error: Sources of error can derive from not stopping the stopwatch on time, inconsistent reading of meter stick, or a slight shift in incline

The experiment contradicts our hypothesis that the distance the ball travels and the time taken to roll down the incline are square relations. The experiment can be further improved by taking multiple meter stick readings and preventing shifts in incline.
 * Conclusion **