Question

Figure 9-34 shows four graphs of position versus time for two bodies and their center of mass. The two bodies form a closed, isolated system and undergo a completely inelastic, one-dimensional collision on an x-axis. In graph 1, are (a) the two bodies and (b) the center of mass moving in the positive or negative direction of the x-axis? (c) Which of the graphs correspond to a physically impossible situation? Explain.

Short answer

1. Two bodies are moving in the positive direction of the x-axis.
2. Center of mass of the bodies is moving in the positive direction of the x-axis.
3. Graph 2 and 3 corresponds to a physically impossible situation.

Step-by-step solution

The given data

Four graphs of position versus time for two bodies and their center of mass.

Understanding the concept of the study of the graph

From the slopes of the lines in graph 1, we can conclude the direction of motion of the 2 bodies and their center of mass. From the characteristics of the center ofmass and the nature of the graph, we can find the graph which corresponds to a physically impossible situation.

a) Calculation of the direction of the motion of the two bodies

From graph 1, we can infer that the slopes of the lines are positive.

Therefore, two bodies are moving in the positive direction of the x-axis.

b) Calculation of the direction of the motion of the center of mass

From graph 1, we can infer that the slopes of the lines are positive.

Therefore, the center of mass of the bodies is moving in the positive direction of the x-axis.

c) Calculation of the physically impossible situations

For an isolated system, the center of mass of the given straight linegraph is betweenx and t. The center of the mass line should lie between the lines for two masses.

Therefore graph 2 and 3 corresponds to a physically impossible situation.