You and a classmate are discussing how much work one must do to lift a box of mass $m$ a vertical distance $h$. Your classmate argues, "You have to exert an upward force on the box at least equal in magnitude to the box's weight $m|\vec{g}|$, and you lift the box upward a distance $h$, so you must do work equal to $m|\vec{g}|_{t}$. But in addition," your classmate continues, "you must increase the box's gravitational potential energy by $m|\vec{g}| h$. Therefore, you must actually do work equal to or greater than $2 m|\vec{g}| h$ to lift the box." What amount of work do you think you need to do on the box to lift it a height $h$ ? Be prepared to defend your response. (Hint: What is the system here?)

Question

Quizplus · Accepted Answer

The work done to lift the box a height $h$ is equal to the increase in gravitational potential energy, which is $mgh$ (where $g$ is the acceleration due to gravity). If you lift the box slowly, the net force (and thus acceleration) on the box is zero, except for the force to overcome gravity, meaning all the work done goes into increasing the box's potential energy, not its kinetic energy.

You and a Classmate Are Discussing How Much Work One mmm

You and a Classmate Are Discussing How Much Work One $m$