A block slides down a frictionless ramp from height h to the ground. How is energy conserved and what is the energy at the bottom?

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Multiple Choice

A block slides down a frictionless ramp from height h to the ground. How is energy conserved and what is the energy at the bottom?

Energy is conserved in a frictionless system: gravity does the work as the block slides down, while the ramp’s normal force does no net work because it acts perpendicular to the motion. At the top, the block has potential energy mgh and essentially no kinetic energy. Since no energy is lost or gained, that potential energy must be transformed into kinetic energy by the time the block reaches the bottom. If we take the ground as the zero of potential energy, the bottom has zero potential energy, so all the energy is kinetic: 1/2 m v^2 = m g h, meaning the total energy at the bottom is m g h. You can also find the speed there: v = sqrt(2 g h). The other statements imply energy is lost to heat, or energy increases, or remains as potential, which doesn’t happen on a frictionless ramp.

Energy is conserved in a frictionless system: gravity does the work as the block slides down, while the ramp’s normal force does no net work because it acts perpendicular to the motion. At the top, the block has potential energy mgh and essentially no kinetic energy. Since no energy is lost or gained, that potential energy must be transformed into kinetic energy by the time the block reaches the bottom. If we take the ground as the zero of potential energy, the bottom has zero potential energy, so all the energy is kinetic: 1/2 m v^2 = m g h, meaning the total energy at the bottom is m g h. You can also find the speed there: v = sqrt(2 g h). The other statements imply energy is lost to heat, or energy increases, or remains as potential, which doesn’t happen on a frictionless ramp.

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