frightened child is restrained by her mother as the child slides down a friction
ID: 1779835 • Letter: F
Question
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 130 N up the slide, the child's kinetic energy increases by 33.0 J as she moves down the slide a distance of 2.1 m. (a) How much work is done on the child by the gravitational force during the 2.1 m descent? (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 2.1 m?
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 = 130 N
Displacement = 2.1 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 = -130 * 2.1 = -273 J
Let Wg = work done by gravitational force.
Total work on the child = Wg + Wm = Wg - 273 J
Also, total work on the child = change in child's kinetic energy = 33 J
Therefore, Wg - 273 J = 33 J
Or Wg = 273 J + 33 J = 306 J
b) In this situation, the work is done only by gravity.
Therefore, total work done = 306 J
Change in kinetic energy = total work done
Or change in kinetic energy = 306 J
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