In this part of the laboratory you will explore the motion of the two masses attached to a string moving over a pulley system. we will assume a frictionless, massless pulley system in modeling the results of our measurenments. you will use the labquest interface along with the motion sensor to track the movement of one of the masses (how does the acceleration of one of the masses compare to the acceleration of the second there will be several single pulley atwood's machine workstations at various tables in the laboratory. each team should find an open one and gather their data at that workstation. teams will be cycling through three different workstations in today's lab. each of the ends of the strings is attached to a 50 g object, one being a hanger to which you can add additional masses. to that hanger various small masses will be added, creating an unbalanced situation and resulting in a non-zero acceleration for the system. your task is to measure the experimental value of the accelerations and compare those values with the model results using the equations given on the previous page it is recommended that you practice the gathering of data for a bit before taking the final data for it is a bit tricky to release the masses and gather good position vs time data with the motion sensor but it can be done. as in previous labs it is recommended that you make sure of the position vs time data only (eliminate the velocity graph from the screen on lq) and do a quadratic regression to fit the data to the kinematic results for uniform acceleration. before you begin review the write-up and make sure you know how to predict the acceleration of the system for a given mass distribution, i. e. the calculated value requested below. use m1 50 g and m2 =60 g as the two masses. the description on the previous page explains the derivation of the motion. derive that expression here: açalculated place the ranger on the floor directly under the hanger with its target card attached. make sur ith the oounter weis simple atwood's machine lease review the discussion of atwood's machine in our text. here is an example found i erway and vuille (10th edition). atwood's machine example 4.11 goal use the second law to solve a simple two-body problem symbolically problem two objects of mass , and m, with m,> are con- nected by a light, inextensible cord and hung over a frictionless pul- ley, as in figure 4.20a. both cord and pulley have negligible mass find the magnitude of the acceleration of the system and the teusion in the cord strategy the heavier mass, m., accelerates downward, in the negative y-direction. because the cord cau't be stretched, the accel erations of the two masses are equal in magnitude, but opposite in direction, so that a, is positive and a, is negative, and og- each mass is acted on by a force of tension t in the upward direction and a force of gravity in the downward direction. figure 4.20b shows frece body diagrams for the two masses. newron's second law for each mass together with the equation relating the accelerations, constitutes a set of three equations for the three unknowns-a ap and t figure 4.20 (example 4jd atwood's machine a) twn hanging ohjects commected by a light sring thas passes over a frictionless palley (he free-hods diagrans for the objects. solution apply the second law to each of the two objects individually (i) ma,7-mg (2) m t- mg substitute a,-a, into equation (2) and multiply both sides by-i: (3) ya-t+ mg add equations (1) and (3), and solve for o t- substitute this result into equation (1