This image of a roller coaster is designed to show important information about potential and kinetic energy. One of these pieces of information is incorrect. Which information is wrong, and why?
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1 point
A. The roller coaster would only have kinetic energy at the point labeled “gravitational potential energy and kinetic energy.”
B. The spot with the “maximum kinetic energy” should be on the lowest point of the roller coaster, at the far left side on the bottom.
C. The roller coaster would only have potential energy at the point labeled “gravitational potential energy and kinetic energy.”
B. The spot with the “maximum kinetic energy” should be on the lowest point of the roller coaster, at the far left side on the bottom. This information is incorrect because the spot with the maximum kinetic energy should be at the bottom of the first hill, not the lowest point of the roller coaster. This is because the roller coaster has the most potential energy at the top of the first hill and this potential energy is converted into kinetic energy as the roller coaster descends down the hill.
which information is correct, though.
The correct information from the given options is:
A. The roller coaster would only have kinetic energy at the point labeled “gravitational potential energy and kinetic energy.”
This statement is correct. At the point labeled "gravitational potential energy and kinetic energy," the roller coaster has its maximum kinetic energy and zero potential energy. As the roller coaster goes up the hill, it gains potential energy, and as it comes down the hill, it converts that potential energy into kinetic energy. Thus, the roller coaster would have both potential and kinetic energy at other points on the track.
If the roller coaster is perfect and has no frictional losses of any sort, then the kinetic energy is max at the lowest point
m g h + (1/2) m v^2 = constant
Yes, you are correct. According to the law of conservation of energy, if the roller coaster is perfect and has no frictional losses, then the total mechanical energy of the system (i.e., the sum of potential and kinetic energy) remains constant throughout the ride. As the roller coaster descends from the highest point, it gains kinetic energy at the expense of potential energy. Therefore, if there were no frictional losses or air resistance, the roller coaster would have its maximum kinetic energy at the lowest point of the track, where all potential energy has been converted to kinetic energy. The equation you mentioned, mgh + (1/2)mv^2 = constant, is the conservation of energy equation for the roller coaster, where m is the mass of the roller coaster, g is the acceleration due to gravity, h is the height of the roller coaster, v is its velocity at any given point.
To determine which information is incorrect about the potential and kinetic energy in the image, we need to review the definitions of these energies and analyze the roller coaster's features.
1. Gravitational potential energy is the energy an object possesses due to its height relative to the ground. Kinetic energy, on the other hand, is the energy of an object in motion.
Based on this, let's evaluate each statement:
A. The roller coaster would only have kinetic energy at the point labeled "gravitational potential energy and kinetic energy."
Explanation: This statement is incorrect. According to the image, the roller coaster does have both potential and kinetic energy at the labeled point. As the roller coaster descends from its highest point, it gains kinetic energy due to its motion, while simultaneously losing potential energy as it decreases in height.
B. The spot with the "maximum kinetic energy" should be on the lowest point of the roller coaster, at the far left side on the bottom.
Explanation: This statement is correct. According to the image, the lowest point of the roller coaster (at the far left side on the bottom) would have the maximum kinetic energy. At this point, the roller coaster has converted most of its potential energy into kinetic energy since it has descended from a higher position.
C. The roller coaster would only have potential energy at the point labeled "gravitational potential energy and kinetic energy."
Explanation: This statement is incorrect. As mentioned earlier, the roller coaster has both potential and kinetic energy at the labeled point. It possesses potential energy due to its height above the ground and kinetic energy due to its motion.
Therefore, the information that is incorrect is statement A: "The roller coaster would only have kinetic energy at the point labeled 'gravitational potential energy and kinetic energy.'". This statement is false because, at that point, the roller coaster has both potential and kinetic energy.