<p> PH111 Newton’s Second Law</p><p>Introduction Newton’s laws of motion can be used to predict the motion of objects under the influence of forces. In this experiment, we will test Newton’s second law using a simple device known as Atwood’s machine. It consists of a pulley, a light string draped around it, and hanging masses placed on both ends of the string.</p><p>We can predict the acceleration using Newton’s second law. The forces involved will be weight, friction, and air resistance. As in a previous experiment, we will ignore the effects of air resistance. We might not be able to ignore the effects of friction.</p><p>Newton’s second law is written as follows:</p><p>ΣF = ma ΣF = total (net) force m = mass a = acceleration</p><p>Newton’s second law can be solved for acceleration:</p><p> a = ΣF/m</p><p>In this case, the weight forces work against one another, so we must subtract to find the net force on the system of hanging masses. The mass is just the total mass of the pair. The acceleration can then be predicted as follows:</p><p> a = (m2g – m1g)/(m2 + m1) a = (m2 – m1)g/(m2 + m1)</p><p>If we include the effects of friction and the mass of the pulley, then the equation for acceleration becomes:</p><p> a = (m2 – m1 – mf)g/(m2 + m1 + ½mp). mp = mass of pulley mf = mass required to overcome friction.</p><p>The above theoretical acceleration can be used to calculate a theoretical value for time. We can use the equation from chapter 3 that relates distance (d), acceleration (a), and time (t).</p><p> d = ½at2 t = √(2d/a) Physics is fun!</p><p>Experimental Procedures</p><p>1) Assemble the Atwood’s machine apparatus as directed. Install “50 gram” hangers on each end and add approximately 100 grams to each hanger. 2) Determine the mass needed to overcome friction by adding mass to one side until the masses move at a constant speed when set in motion by a very slight tug. Be very thoughtful in your analysis of the error in this mass. Clearly justify your estimate of the error. 3) Remove the mass needed to overcome friction, if any. 4) Hold one hanger down on the ground and measure the distance from the bottom of the other hanger to the ground. 5) Add approximately 5 grams to the second mass while holding the string. Release the string and measure the time it takes the second mass to fall to the ground ten times. Compute the average time. 6) Add approximately 5 more grams to the second mass and repeat the previous step. 7) Continue adding approximately 5 grams until the second mass is approximately 175 grams including the mass of the hanger. 8) For each value of the second mass, compute the theoretical acceleration. 9) For each value of the second mass, compute the theoretical time. 10) Graph and compare theoretical and experimental time as a function of m2. </p>