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) the kinetic energy of the block when it has fully compressed the spring will be

Question

Quizplus · Accepted Answer

Since there is no friction, the total mechanical energy of the block-spring system is conserved. When the block reaches the spring, it has only potential energy equal to mgh (where h is the vertical height difference between the starting point and the horizontal line). As the block compresses the spring, its potential energy is transformed into elastic potential energy stored in the spring. When the spring is fully compressed, all of the initial potential energy has been transferred to the spring, and the block has come to a stop. At this point, the total mechanical energy of the system is entirely in the form of elastic potential energy. Since the block has come to a stop, its kinetic energy at this point is zero. Therefore, the correct choice is C.

Assuming the Incline to Be Frictionless and the Zero of Gravitational