An Atwood Machine is a very simple device invented by George Atwood in 1794 as a way to demonstrate Newton’s Laws of Motion. Newton’s Second Law of Motion says that the force required to move something equals the object’s mass times it’s rate of acceleration: F = ma. When Earth’s gravity is the force, you use 9.8 m/s^{2 } for a. This is gravitational acceleration, the rate at which gravity pulls everything towards the center of the Earth.
You can rewrite Newton’s Second Law to solve for acceleration by dividing both sides by m: a = F / m. Acceleration is just what happens when you push on a mass, m, with a force, F.
In this project, you’re going to build an Atwood Machine and see this law in action. You will use the Atwood Machine to verify for yourself the acceleration due to gravity.
Problem: Build a simple Atwood Machine to understand Newton’s Second Law and estimate the pull of gravity.
Materials
 Ring stand
 Pulley (can be found at a hardware store)
 Length of string
 Several masses of different weights (two which should be the same) to which the string can be tied
 Ruler
 Stopwatch
Procedure
 Attach the pulley to the top of the ring stand.
 Tie two masses of equal weight to opposite ends of the string and run the string over the top of the pulley. The string should be long enough so that one mass can rest on the table/ground with the other dangling near the top of the stand.
 Position the masses at different heights from the ground and let go. Do the masses move? What do you think is going on?
 Replace one mass with another that is slightly heavier. Drag the lighter mass down as far as it will go and release. Do the masses move this time? What’s different from before?
 Replace the same mass with one that is slightly heavier still and repeat Step 4. Do the masses move differently? Why or why not?
 Go back to the masses you used in Step 4 – one slightly heavier than the other. Pull the lighter mass down as far as it will go.
 Use a ruler to measure the height of the other mass above the table.
 Grab a stopwatch. Release the mass and start the watch at the same time. As soon as you hear the other mass hit the ground, stop the timer. Do this at least three times, and record your times in a table.
 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}. Record this in the table as well.
 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.
 Calculate the average g from all your trials.
 Replace the mass with at least two other heavier masses and repeat Steps 69.

m_{1} = 
m_{2} = 
Height (m) = 

Time (s) 
Acceleration (m/s^{2}) 
g (m/s^{2}) 
Trial 1 



Trial 2 



Trial 3 



Average 




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