Data analysis Theoretical analysis It is common to compare your experimental data to a theoretical analysis ofthe situation, which often involves considering an ideal case. [The meaning of "ideal" will be explored in one ofthe followup questions.) These instructions will walk you through the process of finding the acceleration in terms of the two masses. At first. you will be working out a purely symbolic expression: you will not be using numbers until aer you have found an expression for the acceleration a in terms of the two masses in: and m2. 1. Draw a free body diagram for each hanging mass. Label the coordinate axes with the +5: direction pointing up. Attach an image [scan or picture] of your free body diagrams here: 2. Apply Newton's second law {1"}, = may) to each mass separately. Note that for the heavier rnassJ the acceleration is negative: oy = -a. This negative sign is crucial to an accurate analysis. 3. Solve each equation for tension. That is, follow the appropriate algebraic steps to get the tension FT by itself on one side ofthe equals sign, and all other quantities [m, a, and g] on the other. 4. The tension pulling up on each mass is the same [this is due to Newton's third law, as alluded to in the overview section of this handout]. The acceleration (a) of each mass is also the same. Set your two equations equal to each other and solve for a. You will ultimately nd the expression ml _ m2 a : m1 + May or something that is similar but mathematically equivalent Note that m1 m2 is the dierence between the two masses, and 1111 + m2 is the total mass. Show your work for all the mathematical steps, starting from Newton's second law. below: 5. Using this relationship, calculate the theoretical acceleration for each trial. Changing mass difference Trial Theoretical acceleration 2 4 8 10 11 12 13 14 15Changing total mass Trial Theoretical acceleration 2 3 4 5 8 9 10 11 12 13 14 15