Assuming the incline to be frictionless and the zero of gravitational potential energy to be at the elevation of the horizontal line, A)the kinetic energy of the block just before it collides with the spring will be equal to mgh. B)the kinetic energy of the block when it has fully compressed the spring will be equal to mgh. C)the kinetic energy of the block when it has fully compressed the spring will be zero. D)the kinetic energy of the block just before it collides with the spring will be kx². E)None of the above statements will be true.

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Quizplus · Accepted Answer

Since the incline is frictionless, there will be no loss of mechanical energy due to friction. Therefore, the total mechanical energy of the block-spring system will be conserved. Initially, the block has only gravitational potential energy, which is given by mgh, where m is the mass of the block, g is the acceleration due to gravity, and h is the height difference between the horizontal line and the initial position of the block. As the block slides down the incline, it loses height and gains speed, which means its gravitational potential energy is converted into kinetic energy. Just before it collides with the spring, the block has zero gravitational potential energy and some kinetic energy. Let this kinetic energy be K.

When the block collides with the spring, it compresses the spring and comes to rest momentarily. At this point, all of the block's kinetic energy is converted into elastic potential energy stored in the spring. As the spring expands, it returns the stored elastic potential energy to the block, which causes it to move upward. When the block reaches its maximum height, it again has zero kinetic energy and some gravitational potential energy, which is equal to the elastic potential energy stored in the spring when it was compressed.

When the block has fully compressed the spring, it comes to rest momentarily again. At this point, all of the block's kinetic energy is converted into elastic potential energy stored in the spring. However, since the block is momentarily at rest, its kinetic energy is zero. Therefore, the correct statement is that the kinetic energy of the block when it has fully compressed the spring will be zero (choice C).

Assuming the Incline to Be Frictionless and the Zero of Gravitational