Equal forces push together the two equal-mass boxes shown in the figure. The table surface is frictionless. Both boxes have the same initial speed, and later both have the same slower speed. Let the system consist of the boxes and the spring. Part A Is the work done on the system positive, negative, or zero? Explain.Part B Is delta E, the change in the system's energy, positive, negative, or zero? Explain.
Question
Equal forces push together the two equal-mass boxes shown in the figure. The table surface is frictionless. Both boxes have the same initial speed, and later both have the same slower speed. Let the system consist of the boxes and the spring. Part A Is the work done on the system positive, negative, or zero? Explain.Part B Is delta E, the change in the system's energy, positive, negative, or zero? Explain.
Solution
Part A: The work done on the system is zero. This is because the forces are internal to the system. The forces pushing the boxes together are equal and opposite, so they cancel each other out. In a frictionless environment, no external work is done on the system.
Part B: The change in the system's energy, delta E, is also zero. This is because the system is isolated and there are no external forces doing work on it. The initial kinetic energy of the boxes is converted into potential energy in the spring when the boxes are pushed together, and then converted back into kinetic energy as the boxes move apart. The total energy of the system (kinetic + potential) remains constant.
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