Roth+Lab+16

Lab 16 Centripetal Force


 * Preliminary Questions:**
 * 1) The object itself is actually traveling at a constant speed in a line rather than a circle. The tangential speed is the natural moment. Circular motion simply involves the natural motion of linear motion being acted upon by some other force, like tension or gravity. Centripetal Force is not a force by itself. It is merely the byproduct of some other force.
 * 2) A change in motion or position per unit time is the derivative of position. The derivative of position is velocity.
 * 3) A force that is directed towards the center of circular motion is called centripetal force.


 * Data:**
 * Trial || Hanging Mass (kg) || Mass of Stopper (kg) || Total Time (s) || Radius (m) || Centripital Force (N) || Period (s) || Circumference (m) || Speed (m/s) ||
 * 1 || .10 || .012 || 11.87 || 1 || 1 || .5935 || 6.2832 || 10.587 ||
 * 2 || .15 || .012 || 10.23 || 1 || 1.5 || .5115 || 6.2832 || 12.2838 ||
 * 3 || .20 || .012 || 9.86 || 1 || 2.0 || .493 || 6.2832 || 12.745 ||
 * 4 || .25 || .012 || 9.62 || 1 || 2.5 || .481 || 6.2832 || 13.063 ||
 * 5 || .30 || .012 || 8.15 || 1 || 3.0 || .4075 || 6.2832 || 15.419 ||
 * 6 || .35 || .012 || 7.77 || 1 || 3.5 || .3885 || 6.2832 || 16.173 ||

Weight of hanging mass= hanging mass x 10 N/kg F= W= .10 x 10 = 1 N
 * Sample Calculations:**
 * Centripetal Force:**

Period= Total time/ number of revolutions Period= 11.87/ 20 = .5935
 * Period by Revolution:**

C= 2 x pi x radius C= 2 x 3.1416 x 1= 6.2832
 * Circumference:**

Speed= Circumference/ Period Speed= 6.2832/ .5935 = 10.587
 * Speed:**


 * Graphs:**

Graph 1.0 shows a positive correlation between speed and centripetal force. Graph 2.0 shows a positive correlation between speed squared and centripetal force. However, the equation of best fit for Graph 1.0 is exponential while Graph 2.0 demonstrates a linear relationship. Since the speed vs. force graph has its variable raised to approximately the second power, it makes sense that the speed squared vs. force graph would have a linear model. This is because the square root of x^2 is x, which is linear. The slope of Graph 2.0 is linear, so its slope is determined by the coefficient of the linear term, which would be .016. The centripetal force is supplied by gravity as well as the mass of the hanging mass. Since the hanging mass is located in the center of the created circle, the weight is also there. The centripetal force follows the weight, so the centripetal force Is directed towards the center of the circle. Since there is a positive correlation between speed and centripetal force, if the speed is increased, then the force required to maintain the circular motion increases. Since x, the speed is raised to the second power in Graph 1.0 to equal y, the force, then doubling the speed would equate to multiplying the centripetal force by 4. The centripetal force for a car going around a circular off-ramp at a constant speed would be supplied by friction. If the speed is too high for the corresponding centripetal force or friction, then the car will get tight as the car will be unable to negotiate the turn. Instead, the car will continue on a relatively linear path as opposed to circular motion. If the car doubles its speed, then the centripetal force will need to be multiplied by four.
 * Analysis:**
 * Application:**