RELEVANT EQUATIONS

REFERENCE Cutnell and Johnson, Chapter 4

DISCUSSION

Figure 6-1: Interactive Physics Window

The Interactive Physics simulation you will investigate consists of a block (mass #1) sliding on a frictionless horizontal surface. The block is connected by means of a cord, which passes around a pulley, to a plummet (mass #2). The apparatus is illustrated schematically in Figure 6-1. The simulation is a computer generated facsimile of the motion with a longer time scale so that the details of its motion can be investigated.

In the first exercise, you will investigate the accelerations of the two masses in several trials by using different mass ratios between them. First, let us look at the principles with which we can predict the accelerations. We draw a free body diagram for each mass, taking into account all the forces that might be acting, as shown in Figure 6-2. Then the Second Law is applied by adding up all the forces in the x- and y-directions and equating them to the mass times the acceleration in each direction. In keeping with convention, we take the +x-axis along the horizontal and to the right, and the + y-axis along the vertical upward.

In the diagram the weights of the bodies are m₁g and m₂g, respectively. The normal reaction force exerted by the horizontal surface is F_N and the tension in the string is T.
 
 

Note that the acceleration vectors are drawn to indicate the expected direction of a in each case, and must be consistent with each other. Thus, m₁ is expected to be accelerated in the horizontal (+ x) direction and m₂ is expected to be accelerated in the vertical (- y) direction. Adding up the forces on each block:
 
 

mass #1:

mass #2:

The two equations involving the acceleration a can be solved simultaneously to give:

                                                                                           (1)