A frightened child is restrained by her mother as the child slides down a fricti
ID: 1695506 • Letter: A
Question
A frightened child is restrained by her mother as the child slides down a frictionless playground slide. If the force on the child from the mother is 120 N up the slide, the child's kinetic energy increases by 30 J as she moves down the slide a distance of 1.8 m.(a) How much work is done on the child by the gravitational force during the 1.8 m descent?
______ J
(b) If the child is not restrained by her mother, how much will the child's kinetic energy increase as she comes down the slide that same distance of 1.8 m?
______ J
Explanation / Answer
a) There are three forces on the child: 1. Normal force by the slide 2. Force of gravity 3. Force applied by the child's mother Work done by normal force = 0 because normal force is perpendicular to the direction of motion. Force by mother = 100 N Displacement = 1.8 m Force by mother is up the slide and the displacement is down the slide. Force by mother is opposite to displacement. Therefore, work done by mother Wm = -100 * 1.8 = -180 J Let Wg = work done by gravitational force. Total work on the child = Wg + Wm = Wg - 180 J Also, total work on the child = change in child's kinetic energy = 30 J Therefore, Wg - 180 J = 30 J Or Wg = 180 J + 30 J = 210 J b) In this situation, the work is done only by gravity. Therefore, total work done = 210 J Change in kinetic energy = total work done Or change in kinetic energy = 210 J Ans: 210 J