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 is no loss of mechanical energy. This means that the initial potential energy of the block (mgh) is converted completely to kinetic energy as it slides down the incline. At the bottom point, the block has no potential energy and maximum kinetic energy. As it moves up the incline, its kinetic energy is gradually converted back to potential energy until it reaches the point where it has fully compressed the spring. At this point, all of its initial kinetic energy has been converted back to potential energy, and this potential energy is stored in the compressed spring. Therefore, the kinetic energy of the block when it has fully compressed the spring will be zero.

Assuming the Incline to Be Frictionless and the Zero of Gravitational