1. An Atwood’s machine consists of two blocks connected by a light string that passes over a frictionless pulley of negligible mass, as shown in the figure above. The masses of the two blocks,M1 and M2, can be varied.M2 is always greater than M1.
(a) On the dots below, which represent the blocks, draw and label the forces (not components) that act on the blocks. Each force must be represented by a distinct arrow starting on and pointing away from the appropriate dot. The relative lengths of the arrows should show the relative magnitudes of the forces.
(b) Using the forces in your diagrams above, write an equation applying Newton’s second law to each block and use these two equations to derive the magnitude of the acceleration of the blocks and show that it is given by the equation:a=(M2-M1)/(M1+M2)g
The magnitude of the acceleration a was measured for different values of M1 and M2, and the data are shown below.
(c) Indicate below which quantities should be graphed to yield a straight line whose slope could be used to calculate a numerical value for the acceleration due to gravity g.
Use the remaining rows in the table above, as needed, to record any quantities that you indicated that are not given.
(d) Plot the data points for the quantities indicated in part (c) on the graph below. Clearly scale and label all axes including units, if appropriate. Draw a straight line that best represents the data.
(e) Using your straight line, determine an experimental value for g.
The experiment is now repeated with a modification. The Atwood’s machine is now set up so that the block of mass M1 is on a smooth, horizontal table and the block of mass M2 is hanging over the side of the table,as shown in the figure above.
(f) For the same values of M1 and M2, is the magnitude of the tension in the string when the blocks are moving higher, lower, or equal to the magnitude of the tension in the string when the blocks are moving in the first experiment?
____Higher ____Lower ____Equal to
Justify your answer.
(g) The value determined for the acceleration due to gravity g is lower than in the first experiment. Give one physical factor that could account for this lower value and explain how this factor affected the experiment.