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A child is at rest at the top of a waterslide. A graph modeling the child-Earth system’s starting kinetic energy \[(\text{K})\] and gravitational potential energy \[(\text{U}_\text{g})\] is shown below.

A bar graph with categories labeled K and U g. The y-axis is labeled energy (J). 5 horizontal lines divide the y-axis into equal segments. The y-axis is labeled, from bottom to top, 0, 100, 200, 300, 400, 500.
The bar above the U g category goes from zero to 500. There is no bar above the K category.
The child slides down the waterslide. The zero reference level for gravitational potential energy in the child-Earth system is the surface of the water, as shown below.
A girl has just left the end of a waterslide and is in midair above the water in a pool. The surface of the water below the girl is marked with a horizontal dotted line labeled U g equals zero.
Which graph could represent the energy of the child-Earth system when the child is at the position shown in the image above?
Assume frictional forces are small enough to ignore.
Choose 1 answer:
Choose 1 answer:
(Choice A) The same bar chart from above now shows 300 J of K and 100 J of U g.
A
The same bar chart from above now shows 300 J of K and 100 J of U g.
(Choice B) The same bar chart from above now shows 500 J of K and 0 J of U g.
B
The same bar chart from above now shows 500 J of K and 0 J of U g.
(Choice C) The same bar chart from above now shows 400 J of K and 100 J of U g.
C
The same bar chart from above now shows 400 J of K and 100 J of U g.
(Choice D) The same bar chart from above now shows 500 J of K and 200 J of U g.
D
The same bar chart from above now shows 500 J of K and 200 J of U g.

1 answer

To determine the correct energy state of the child-Earth system when the child is in midair above the pool after sliding down the waterslide, we need to consider the conservation of mechanical energy, which states that the total mechanical energy (kinetic + potential) in the absence of non-conservative forces (like friction) remains constant.

  1. Initially, the child has 0 J of kinetic energy (K) at the top of the waterslide and 500 J of gravitational potential energy (U_g).
  2. As the child slides down the waterslide, gravitational potential energy converts to kinetic energy.

At the moment the child leaves the end of the waterslide and is in midair, we can use the conservation of energy:

  • Total energy at the top = Total energy while in midair
  • Initial energy = K + U_g = 0 J + 500 J = 500 J.

Since the child is now in midair and just about to enter the water, U_g will be 0 at the surface of the water because that's our reference point. Therefore:

  • U_g = 0 J.
  • The child must have all 500 J converted into kinetic energy.

Thus, the energy configuration when the child is in midair above the water should be:

  • K = 500 J
  • U_g = 0 J

Based on the answer choices, the correct graph representation that reflects this energy state is:

(Choice B) The same bar chart from above now shows 500 J of K and 0 J of U_g.