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.
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.
Solution
The work done on the system is zero. Here's why:
Work is defined as the force applied to an object times the distance over which it is applied, and it is also equivalent to the change in kinetic energy of the object. In this case, the forces are applied internally within the system (the boxes and the spring), and they are equal and opposite, so they cancel each other out. This means that the net force applied to the system is zero, so the work done on the system is also zero.
Furthermore, the kinetic energy of the system doesn't change. The boxes start with some initial speed and end with a slower speed, but the energy they lose is stored as potential energy in the spring. When the spring releases, this energy is converted back into kinetic energy. So, the total energy of the system (kinetic + potential) remains constant, which again suggests that the work done on the system is zero.
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