LVang+-+L14+-+Centipetal+Force+Lab

Lue Vang Mr. Kellogg AP Physics - Pd. 7 28 February 2012 Performed On: 23 February 2012 Lab Partners: Sebby Alvarez, Arielle Roth, Lue Vang

**Centripetal Force Lab **

This lab will study the change in centripetal force, period, and speed of circular motion as the hanging mass at the bottom of the apparatus is changed.
 * __Purpose: __**

 **__Background:__**  Centripetal force can lead to circular motion as an object is “pulled in” to the center of the circular path by centripetal acceleration. The revolving object does not spiral inward because inertia keeps the object in orbit. For centripetal motion, the tangential velocity of the orbit object may be constant and still have acceleration because the object has a change in direction. When its circular motion is analyzed in the form of vectors, it is apparent that the velocity of the (x) and (y) coordinates change conversely to create the change in direction. While spinning, a period is the time the spinning object takes to make one revolution of the circumference.

Preliminary questions:


 * 1) Circular motion at constant speed is not a natural state of motion because there is force acting on it to keep it in its “constant motion.”
 * 2) A change in motion per unit of time is acceleration, which is associated with net force through Newton’s second law of F = ma where (F) is force, (m) is mass, and (a) is acceleration.
 * 3) A force that is directed towards the center of circular motion is called the centripetal force.

Seeing that the mass is hanging, it is experiencing an acceleration due to gravity, so the Newton’s second law says that F = ma, thus changing the mass of the hanging weight will change the force needed to spin the stopper. Spinning the stopper will create a force that pulls the weight up the tube due to the inertia of the orbiting stopper. That being said, the more weight hanging at the bottom, the more force will be needed to bring the stopper up to the position marked by tape on the string, which leads to a faster spin, which results to shorter periods.
 * __<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Hypothesis: __**

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> In other words, the more weight that hangs, the more force is needed, the faster the stopper will orbit, and the shorter the periods.

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> **__Apparatus:__**
 * <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Nylon Cord (1.75m)
 * <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Rubber Stopper (1)
 * <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Glass Tube Wrapped With Tape (1)
 * <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Roll of Tape (1)
 * <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Crocodile clip (1)
 * <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Adjustable masses (1)

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> Take the cord and tie the stopper to the top end. Take the bottom end of the cord and insert it through the glass tube. Measure 1 meter from the stopper and place a tape on the cord at that spot. Attach a crocodile clip at the bottom end of the cord and attach you weight.
 * __<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Procedure: __**

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">With the weight attached, spin the apparatus until the tape on the cord moves to just below the glass tube and stays there. Meanwhile, the stopper should be spinning at a constant speed. Spin the stopper for 20 revolutions and record the time along with the radius of the circle. Complete the process with 100g weights hanging at the bottom that increase in increments of 50g until it reaches 350g.

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> **__Data:__** <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> Table 1.0
 * ** Centripetal Force Data ** ||
 * ** Trial ** || ** Hanging Mass (kg) ** || ** Mass of Stopper (kg) ** || ** Total Time (s) ** || ** Radius (m) ** ||
 * ** 1 ** || 0.10 || 0.12 || 11.87 || 1.0 ||
 * ** 2 ** || 0.15 || 0.12 || 10.23 || 1.0 ||
 * ** 3 ** || 0.20 || 0.12 || 9.86 || 1.0 ||
 * ** 4 ** || 0.25 || 0.12 || 9.62 || 1.0 ||
 * ** 5 ** || 0.30 || 0.12 || 8.15 || 1.0 ||
 * ** 6 ** || 0.35 || 0.12 || 7.77 || 1.0 ||

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Table 2.0
 * ** Centripetal Force Calculations ** ||
 * ** Trial ** || ** Centripetal Force (Fc) (N) ** || ** Period (s) ** || ** Circumference (m) ** || ** Speed (m/s) ** ||
 * ** 1 ** || 1.00 || 0.594 || 6.28 || 10.58 ||
 * ** 2 ** || 1.50 || 0.512 || 6.28 || 12.28 ||
 * ** 3 ** || 2.00 || 0.493 || 6.28 || 12.74 ||
 * ** 4 ** || 2.50 || 0.481 || 6.28 || 13.06 ||
 * ** 5 ** || 3.00 || 0.408 || 6.28 || 15.41 ||
 * ** 6 ** || 3.50 || 0.389 || 6.28 || 16.16 ||

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> Centripetal Force (N) = weight of hanging mass = hanging mass * 10 N/kg <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> i.e) T1 = 0.01 * 10 = 1 N <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> *T1 = trial 1

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> Periods of Revolutions(s) = total time / 20 revs <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> i.e.) T1 = (11.87) ÷ 20 = .594 s

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> Circumference (m) = 2 * 3.1416 * radius <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> i.e.) T1 = 2 * 3.1416 * 1 = 6.28 m

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> Speed (m/s) = circumference / period <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">i.e.) T1= 6.28 ÷ .594 = 10.58 m/s



<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">In this lab, the experiment allows the analysis of centripetal force, which is provided by the weight of the hanging mass (F=ma). This being the case, the string is being pulled down through the glass tube, so the force acting on the spinning stopper is directed to the center of the circle created by the spinning stopper. According to Graph 1.0, increasing the speed of revolution of the stopper increases the force needed to keep the stopper moving around. In fact, the relationship between speed and force seems to be exponential by a power of 2, so doubling the speed of revolution would likely quadruple the original centripetal force. All in all, as the speed of the revolution increases, the centripetal force required to keep the object in orbit is increased by a power of two of its rate.
 * __<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Analysis: __**

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">In a real life application, if a car were to be going around an off-ramp at constant speed, the centripetal force will be one that acts in the direction toward the center of the car’s circular motion, friction. If the speed is so high that the centripetal force is greater than that which can be provided by the road, the car will skid off and break from its circular motion. According to this lab, doubling the car’s speed will require four times as much of the original centripetal force to make the turn.

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> **__Conclusion:__** <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">From the lab, the increasing the mass of the hanging weight decreases the time required for the stopper to make twenty revolutions. After calculating centripetal force, the results show that centripetal force increases as the weight of the hanging mass increases. This is fitting because the speed of the stopper apparently increases as the weight increases, thus indicating a greater force. Obviously, the grater speeds then shorten the period of the object’s constant circular motion. All said, the lab hypothesis is supported.

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">In analyzing centripetal force, it is apparent that increasing the speed of the orbiting object will result in a greater centripetal force needed to keep the object in constant circular motion. Centripetal force is mass multiplied by centripetal acceleration so F = ((mv)2)/2. That being the case, the centripetal force of the system should increase exponentially by a power of two as the speed of the orbiting object, the stopper, increases just as Graph 1.0 suggests.

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">In retrospect, the lab data may be a bit off because the acclaimed scientist spinning the stopper flail had to estimate the constant speed required to bring the tape up to just the right spot. Nonetheless, the results are close enough to give good results. The accuracy of the data can be improved by conducting more trials, but such is not completely necessary here.