1. Rolling Friction

2. How to solve for initial velocity.
Using our grid analysis, we can set up the equation to solve for initial velocity.
Equation to use
Displacement
Time
Initial velocity
Final velocity
Acceleration
vf = vi + at x
d = ½ (vf + vi)t
d = vit + ½ at2
vf2 = vi2 + 2ad
Equation to use
Displacement d
Time t
Initial velocity vi
Final velocity vf
Acceleration a 1.

3. Solving for initial velocity
From our experiment, we measured displacement and time. We let the ball come to a complete stop, so we have the final velocity. From our list of 4 equations, we should choose the 2nd equation. d = ½ (vf + vi) t
Equation to use
Displacement d
Time t
Initial velocity vi
Final velocity vf
Acceleration a 1.  x ?  x 

4. Solving for initial velocity
d = ½ (vf + vi) t Rearrange the equation to solve for vi. Multiple both sides to remove the ½ , we get 2d = (vf + vi) t Divide both sides by t, we get 2d/t = vf + vi Subtract both sides by vf, we get 2d/t – vf = vi Since vf = 0, the final equation is vi = 2d/t

5. Solving for acceleration
Repeat the process to solve the acceleration From our list of 4 equations, we should choose the 4th equation. vf2 = vi2 + 2ad
Equation to use
Displacement d
Time t
Initial velocity vi
Final velocity vf
Acceleration a 1.  x x   ?

6. Solving for acceleration
vf2 = vi2 + 2ad Rearrange the equation to solve for a. Subtract both sides by vi2, we get vf2 – vi2 = 2ad Divide both sides by 2d, we get (vf2 – vi2 )/2d = a Since vf = 0, the final equation is vi2 /2d = a Knowing that this is “deceleration”, use negative a = - vi2 /2d (note: be cautious when entering values into the calculator. Put parenthesis around the 2d  - vi2 /(2d) because it is in the denominator)

7. Alternative to getting acceleration?
Can we use another equation to get acceleration without using the initial velocity?

8. Solving for the coefficient of rolling friction
Once we have our acceleration, we can use the equation m = a/g where a is the acceleration of the object and g is the acceleration due to gravity.

9. Conclusion
Final conclusion about the rolling objects. Which characteristics of the object do you think was the most responsible for the largest deceleration (leading to the greatest coefficient of rolling friction) of the object? size, mass, smoothness, etc.

10. Final thoughts
What do you think would happen if instead of carpet, we were using the gym floor. Would the results be the same? Would the properties of the object change the out?