Saturday, May 10, 2008

Irodov Problem 1.151

The tension in the string when it is compressed by a length x is given by . Mass m1 is now pressed against the wall which offers a normal reaction of N. to oppose the force with which the spring pushes it into the wall . As soon as mass m2 is released, the spring will push it away from the wall and so m2 will begin to accelerate. As soon as m2 the spring reaches it uncompressed state there is no tension in the string and so the normal reaction offered by the wall m1 on becomes 0. At this m1 point breaks free from the wall.

Since no work is being done by external forces on the system of masses and spring, its energy is conserved. Initially the energy stored in the system is and this energy will be conserved.

As the point when reaches back to the spring's uncompressed position, suppose than mass m2 is moving with a speed v. At this point mass is m1 stationary and has 0 speed. The total kinetic energy is given by . So we have,

The velocity of the center of mass is thus given by

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