YAA+Group+3

Abstract (Yuriy)When two unequal masses are connected with a strong, light cord that passes over a pulley of negligible mass, the arrangement is called Atwood's machine. This device is used for diluting and measuring acceleration due to gravity. If mass one is greater than mass two and the system is released from rest, the entire system will have the same acceleration. Pulleys change the direction of tension vectors, and the magnitude of the tension everywhere in in the cord has the same value. Since gravity is acting on the entire system, the larger mass produces a larger force on the cord than the smaller mass, causing the pulley to lower the heavier mass. This means the net force of the system is acting down on the side of the larger mass.

Objective (Andrew) By using the Atwood machine we should be able to determine acceleration and therefore study Newton's Second Law of motion. In the machine, weuse the difference in weight of 200g masses + # paper clips on both sides to create an acceleration. the difference in paper clips and therefore weight would allow an acceleration by the heavier mass being dropped from the top pulling the lighter mass upward.This lab is use to help us understand F = ma and by us changing the mass and therefore affecting acceleration we are also able to calculate the force upon each mass. by the end of this lab we hope to understand the relationship between F (force) M (mass) and A (acceleration).

Procedure (Andrew)

1. Use 2 masses of 200 g each on both sides of the Atwood machile. Add 15 paperclips to both sides. This total mass is to remain constant throughout the experiment. 2. Determine the force of friction on the pulley by transferring one clip at a time from one side to the other until the system moves at a constant speed when given a slight push. Calculate the frictional forces on the pulley by subtracting the two masses. Record value. 3. Now transfer two more clips from the ascending side to the descending side. You now have a net force acting on the system while also compensating for friction. 4. begin the experiment with the ascending mass on the floor. Release the descending mass, stopping the timer when it reaches the floor. Record the time and the distance between the two masses. Repeat two mroe trials. Determine and record the average of there 3 trials. Calculate the acceleration of the system using equation (3). 5. Transfer 2 more clips fromt he acsending side to the descending side. Repeat procedure #4 again using 3 separate trials. 6. Continue transfering mass from the ascending side to the decsending side for a total of 5 trials or out of paper clip. 7. Conpute acceleration of the systemm using €F 8. Using the acceleration of procedure 4, plot a graph of acceleration vs. (m1 - m2) / (m1 + m2)  

Materials (Yuriy)


 * 1) Pulley
 * 2) Light weight cord
 * 3) Two 200 gram weights
 * 4) Thirty paper clips of the same size
 * 5) Timer
 * 6) Meter stick

Data (Adam) Mass of One Paperclip = 2.3g Distance = .715m Friction = î( mass)g Friction = .36064N 
 * Trial # || Mass Transferred (g) || Total Mass Difference (g) || Net Force (N) || Time 1 (sec) || Time 2 (sec) || Time 3 (sec) || Average Time (sec) || Experimental ||
 * ||  ||   ||   ||   ||   ||   ||   || Acceleration (m/s2) ||
 * 1 || 4.6 || 46 || 0.09016 || 2.76 || 3.34 || 2.54 || 2.88 || 0.172405478 ||
 * 2 || 4.6 || 55.2 || 0.18032 || 2.26 || 2.44 || 2.3 || 2.333333333 || 0.262653061 ||
 * 3 || 4.6 || 64.4 || 0.27048 || 1.9 || 2.1 || 2.08 || 2.026666667 || 0.348153999 ||
 * 4 || 2.3 || 69 || 0.31556 || 1.86 || 1.96 || 1.92 || 1.913333333 || 0.390620258 ||

Analysis (Adam) The slope of the line on the graph was about 4.44. This is supposed to be the experimental value for the acceleration due to gravity. Gravity is universally accepted as 9.8m/sec 2. This seems to be off by about a factor of about 2. We might have had some errors in timing or friction.



Conclusion (Adam)
 * 1) We can keep the total mass constant and not have to readjust the mass differences and sums for every single trial.
 * 2) Perhaps there were just human errors in doing the experiment. There could also be drag that we didn't account for as well as shifts in acceration due to some small swinging of the weights on the string.
 * 3) The tension on the ascending side is about 2.12N and about 2.48N on the descending side. They are different because we had to account for friction on the descending side.
 * 4) The lighter the pulley, the less friction there will be between the axle and the support. Our values will be better if the friction is lower.