Objective Verify Newton's Second Law of Motion for connected masses. Materials Pulley string Theory In order to slow down a falling object, we need to apply a force to the object in the upward direction. This can be done using an Atwood's machine. The Atwood's Machine is simply a pulley of negligible inertia and friction over which are suspended two masses. When the masses are unequal, the system will accelerate in the direction of the heavier mass. In this experiment, you will measure the acceleration and compare it to that predicted by Newton's second law (EF = ma)-you will compare aexp to atheo. For the purposes of this experiment, we shall assume that the acceleration is constant. Therefore, if the system begins at rest, y is the distance traveled and t is the time it takes to go a distance of y. You will measure y and t to calculate the acceleration, using the constant acceleration equations (kinematic equations). Procedure Start out with 200g for m₁ and m₂. Place m₂ on the floor. Measure the distance y, from the bottom of m₁ to the floor. Now begin the experiment. Hold mi to the floor. Place one additional 5g mass on m₂. Let go of m₁ and time the descent of m₂ to the floor: start the stop watch at the instant you let the weights go, and stop it at the instant when m2 strikes the floor. Repeat the experiment 3 times, to insure consistent times. Then repeat with 5g more mass added to m₂. Run trials with 5, 10, 15, and 20 grams added to m2. Data and Analysis 2y a experimental t² For two different masses connected by a string over a pulley, with m₂>m₁, the acceleration is given by: - m₁ (kg) masses Measured value of y %difference=- (from a kinematic equation) a=9, m₂ (kg) meter stick stopwatch 1200 1205 ,200 210 1200 1215 0 2|atheory-expl atheory+aexp 1105 (m) t (sec) M 2-MI mp tm z 1 x 100% (Do all calculations in MKS system) 4183 3.15 2.72 aexperimental (m/s²) (see next page) atheoretical (m/s²) % difference BÄÄÄÄÄÄÄÄÄÄÄÄÄ CHAX only 3 onsdie ed and Donated by: Applying Newton's second law to the Atwood's Machine: ΣF=m, a T-m₁g=m₁a (1) ΣF=m,a -T+m₂g=m₂a(2) Sum 1 and 2: T-m₁g=m₁a +(-T+m₂g=m₂a) m₂g m₁g=m₁a+m₂a (m 2-m,)g=a(m 1+m₂) solve for the theoretical acceleration a: a=g m₂-M₁ m₁ +m₂ Free-body diagram for #1 mg m₂ Free-body diagram for Ill Questions 1. Why should the pulley be as light as possible as well as frictionless? 2. What is the difference between uniform motion and uniformly accelerated motion? 3. For the last trial of your experiment, calculate the upward tension force exerted by the string on m₁. Use the theoretical acceleration for that run, which you calculated. 4. For the same trial, calculate the upward tension force exerted by the string on m₂. 5. Comment on the two upward tension forces you found. Are they the same or different? Should they be the same or different? Explain.