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Lab 4: Newton's 2"d Law (Atwood's Machine) Purpose: In this lab, we will learn to use the setup called the Atwood's Machine to prove Newton's 2"d Law. We will also learn how to calculate the experimental acceleration of an object. Equipment: Two Pulleys, Vertical Rod, Clamps, Hangers, Slotted weights, Stopwatch, Meter Stick Theory: According to Newton's 20 law of motion, the Acceleration of an object (a) is directly proportional to the Total External Force on the object (F) and inversely proportional to the mass of the object (m) - -> a = F/m. In this lab, we will hang weights over a pulley and connect it to another weight over another pulley. The picture looks like the following: M In this situation, the acceleration of both hangers will be the same since they are attached, and it will be equal to, atheor. = (M - m)g/(m + M) Ex. If M = 125 grams, m = 40 grams, then a = (125 - 40)(9.8)/(125 + 40) = 5.05 m/s? The big M will accelerate downward at 5.05 and the small m will accelerate upward at 5.05! This gives us the Theoretically Expected acceleration. In order to get the Experimental acceleration, we time how long it takes the small m to go up a certain distance, S. Then we use the equation, aexper. = 28/t. In order for this equation to work, you must start the timer the SAME INSTANT that you let go of the hangers so that the initial v = 0. Ex. In the above example, if the small m went up 70 cm in 0.52 seconds, then aexp = 2(.70)/.52" = 5.18 m/s'. The % error would be = 100% x |5.18-5.05//5.05 = 2.57% Procedure: Cut a length of string long enough so that one hanger (M) can be at the top and the other hanger (m) be at the bottom near the floor on the other side. Screw 2 pointers to the meter stick and place the bottom pointer where the BOTTOM of the hanger (m) is. Then screw the top pointer about 70 cm above this screw. Release the hangers and start the Stopwatch at the same time. When the BOTTOM of the hanger (m) has reached to the top screw position, stop the stopwatch and the hangers. Don't allow the falling weig g weight to hit the floor!!! Record this time and repeat it again to obtain an average time. Repeat with different combinations of m and M