If there’s not a large enough difference, there’s not enough net force to overcome the friction. You can get an idea of how much friction is involved by figuring out how small a mass difference you can have without the masses falling. There is friction in the bearings and it takes energy to get something rotating. There are many places where energy gets lost, mostly in the pulley. This is because your Atwood Machine is not a perfect system. How close did you get? You probably notice that you got something a little different every time and that your final average value is lower than the “accepted value.” Solving for g gives you the equation you used to figure out the gravitational acceleration above. Putting those two effects together, the final acceleration equals: a = ( ( m 1 - m 2) / ( m 1 + m 2)) g. The net force pulling down is the amount that would be felt if gravity were pulling on something that weighed the same as the difference between the two masses: F = ( m 1 - m 2) g.īut the force is pulling on both masses simultaneously, so the acceleration equals what you would get when applying this force to something that weighed the same as the sum of the masses: a = F / ( m 1 + m 2). Mass 1 feels its own weight pulling down, and the weight of the other mass pulling up. Once the masses are unequal, the forces become out of balance. Everything is in equilibrium-no force means no motion. This is true no matter how high or low the masses are. Since the gravitational forces are the same, that means m 1, for example, is feeling the same force pulling up as it does pulling down. The tension on mass 1 ( m 1) is caused by the gravitational force on mass 2 ( m 2). With equal-weight masses set up, all the forces are in balance. There are three forces at work here: the forces of gravity on both masses and the tension in the string connecting them. When calculating g, you should get something close to the accepted value of 9.8 m/s 2, though it will most likely be a bit less because of friction in the pulley. As the difference in the masses increases, the speed with which it hits the ground increases as well. When the weights are unequal, the masses will move so that the heavier one falls. With equal masses, the weights will not move. Replace the mass with at least two other heavier masses and repeat Steps 6-9.Calculate the average g from all your trials.Calculate the acceleration due to gravity with the equation: g = a (m 1 + m 2 / m 1 - m 2), where m 1 and m 2 are the heavier and lighter masses, respectively, and a is the acceleration from step 7.For each drop, calculate the acceleration of the masses using the equation: a = 2h / t 2, where h is the height of the mass before being dropped (in meters), t is the time it took to fall (in seconds), and a is the acceleration in m/s 2.Do this at least three times, and record your times in a table. As soon as you hear the other mass hit the ground, stop the timer. Release the mass and start the watch at the same time.
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