Ball+on+incline+Nathan+Campbell+and+Tyler+Naughton

Title of Lab: Ball on Incline

Researchers: Nathan Campbell and Tyler Naughton

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

Research:

__Variables__//:// t= time Δx = displacement g= force of gravity (about 9.81 m/ s^2) vi = initial velocity a=acceleration m=mass

Displacement can be found through the kinematics equation: **Δx ** **=(** **vi *** ** t)+(1/2)at^2 **

In this experiment, initial velocity is determined to be zero, because the ball is at rest at the beginning of the test. Therefore the equation can be altered:

We can solve for //t//, creating the equation:
 * Δx ****=(1/2)at^2 **
 * t^2=2Δx **** /a **

Source//: http://farside.ph.utexas.edu/teaching/301/lectures/node48.html//

Based on the picture, we see that acceleration is not directly based off of weight (//mg//), but rather a component of //mg, mg sin//θ. Acceleration can be determined using ** mgsinθ **

According to Newton's Second Law, the sum of all forces in a system is equal to the mass of the system times acceleration: ** ΣForces=mass x acceleration ** Assuming negligible friction, ** mgsinθ=ma ** We can divide out the masses from both sides of the equation, creating the equation **a=g**** sinθ **

Therefore, we can determine the relationship between time and distance on an incline using the angle of inclination and the gravitational constant and our original kinematics equation: ** t^2=2 ****Δx **** /(g x sinθ) [ which can be simplified to ****t= ****<span style="font-family: Arial,Helvetica,sans-serif;">√(2Δ ****<span style="font-family: Arial,Helvetica,sans-serif; line-height: 1.5;">x/(g x sinθ) ] **

Hypothesis:

The time it takes for the ball to roll down a certain length of the incline is proportional to the distance by the equation
 * t^2=2<span style="background-color: #ffffff; color: #444444; font-family: arial,sans-serif; font-size: small; line-height: 1.5;">Δx **** /(g x sinθ) **

Procedure: Materials (Tennis ball, Stopwatch, chair, books(or any flat item), chair/table, plank, 2 meter sticks, spring scale)

1.Place the plank with one side on the chair/table and the other end on the floor. In our experiment, this created an angle of 20 degrees. 2. Place two meter sticks along one side of plank and make sure they are secure (do not allow the meter sticks or the person's hands holding the meter sticks to interfere with the ball as it rolls down the plank.) 3.Place an object at the end of the plank to stop the ball (make sure it is touching the end of the plank) 4. Have a person release the ball and record the time at a specified length along the plank 5.Record the time it took at that specified length in data chart. 6.Repeat steps 7 and 8 at different lengths along the plank (at least 5 data points/lengths).

Data:


 * Distance Traveled (cm) || Time (seconds) ||
 * 0 || 0 ||
 * 10 || 0.25 ||
 * 20 || 0.38 ||
 * 30 || 0.42 ||
 * 40 || 0.50 ||
 * 60 || 0.64 ||
 * 70 || 0.68 ||
 * 80 || 0.75 ||

Data Analysis:

A graph of our data presents a shape close to a square root curve. In order to create a more linear shape to our graph (this will help determine a line of best fit), we squared the time


 * [I could not get the graph to move to true (0,0), but it technically starts at (0,0)]

We then determined the line of best fit for this graph:
 * y=0.081x-0.1061**

The slope of the line of best fit is approximately 0.08 cm/s^2 Largest amount of error happens in the range of 25-45cm.

From this information, we can determine our experimental g-value through the equation 2/(slope*sinθ) Our experimental g-value is about 7.3 Comparing this experimental value to our theoretical values, our percent error is 26%

Possible causes for such extreme error include:
 * Not maintaining a constant angle
 * Restrictions in the reaction time it takes to start and stop the stopwatch. It is very difficult to manually, using a stopwatch, measure the time of an object in such a short time window
 * The possible effect of friction between the tennis ball and plank
 * Stop Watch has a limited accurate reading
 * Original velocity was based off an eye view causing for a miss value in dependent variable.

Conclusion:

The data collected does not support our hypothesis. By correcting our error and reevaluating our research and formulas, we may be able to derive the a supportable hypothesis that explains the data.