a. at which point does the roller coaster have the most kinetic energy?
4
b. at which point does the roller coaster have the most potential energy?
1
c. describe what is occurring as the cart moves from point 1 to point 2.
d. describe what is occurring as the cart moves from point 4 to point 5.
e. compare the amount of potential energy present at points 1, 3, and 5.
f. from point 1 to point 5, what happens to the total amount of energy?

Question

Accepted Answer

### Part A
# Explanation:
## Step1: Recall energy concepts
Kinetic energy ($KE$) is related to motion, $KE = \frac{1}{2}mv^2$. Potential energy ($PE$) related to height, $PE = mgh$. At lowest height (closest to ground), speed is highest (since $PE$ converts to $KE$) if no non - conservative forces (like friction) are considered. Point 4 is the lowest point among 1,2,3,4,5. So at point 4, speed is maximum, hence $KE$ is maximum.
# Answer: 4

### Part B
# Explanation:
## Step1: Recall potential energy formula
Potential energy $PE = mgh$, where $h$ is height above a reference point. Higher the height, more the $PE$. Point 1 is the highest point among 1,2,3,4,5. So at point 1, $h$ is maximum, hence $PE$ is maximum.
# Answer: 1

### Part C
# Explanation:
## Step1: Analyze energy conversion from point 1 to 2
At point 1, the roller - coaster cart has high potential energy (due to high height) and low kinetic energy (starts from rest or low speed at the peak). As it moves from point 1 to point 2 (which is lower in height), the potential energy ($PE = mgh$) decreases because the height ($h$) decreases. This decrease in potential energy is converted into kinetic energy ($KE=\frac{1}{2}mv^2$), so the kinetic energy increases (the cart speeds up) as it moves down the slope from point 1 to point 2. In other words, gravitational potential energy is being converted into kinetic energy as the cart descends.
# Answer: As the cart moves from point 1 to point 2, gravitational potential energy (due to its height at point 1) is converted into kinetic energy. The cart's height decreases, so potential energy decreases, and its speed increases, so kinetic energy increases.

### Part D
# Explanation:
## Step1: Analyze energy conversion from point 4 to 5
Point 4 is a low - height point (so low potential energy, high kinetic energy). As the cart moves from point 4 to point 5, the height of the cart increases. According to the formula for potential energy $PE = mgh$, as $h$ increases, the potential energy of the cart increases. Since the total mechanical energy (in the absence of non - conservative forces like friction) is conserved, the kinetic energy of the cart decreases (because $KE=E_{total}-PE$ and $PE$ is increasing). So the cart is moving up a slope, kinetic energy is being converted into potential energy, and the cart slows down as it gains height.
# Answer: As the cart moves from point 4 to point 5, kinetic energy is converted into potential energy. The cart's height increases, so potential energy increases, and its speed decreases, so kinetic energy decreases (the cart slows down as it moves up the slope).

### Part E
# Explanation:
## Step1: Recall potential energy formula
Potential energy $PE = mgh$. The height of the cart at a point determines its potential energy (assuming mass $m$ and gravity $g$ are constant). Point 1 is the highest among points 1, 3, and 5. Point 5 is lower than point 1 and point 3 (from the diagram's general shape, point 3 is at a higher height than point 5). So the potential energy at point 1 is the highest, then at point 3, and then at point 5. Mathematically, if $h_1>h_3 > h_5$, then $PE_1=mgh_1$, $PE_3=mgh_3$, $PE_5=mgh_5$, so $PE_1 > PE_3>PE_5$.
# Answer: The potential energy at point 1 is the greatest, followed by point 3, and then point 5 (i.e., $PE_{1}>PE_{3}>PE_{5}$) because potential energy ($PE = mgh$) depends on height, and point 1 is the highest, point 3 is at an intermediate height, and point 5 is the lowest among these three points.

### Part F
# Explanation:
## Step1: Recall conservation of mechanical energy
In an ideal situation (without friction or air resistance), the total mechanical energy $E_{total}=KE + PE$ is conserved. However, in a real - world roller - coaster, there are non - conservative forces like friction and air resistance that do work on the cart. These non - conservative forces convert mechanical energy into other forms of energy (like heat and sound). So as the cart moves from point 1 to point 5, due to the work done by non - conservative forces, the total amount of mechanical energy (kinetic + potential) decreases.
# Answer: From point 1 to point 5, the total amount of mechanical energy (kinetic + potential) decreases. This is because non - conservative forces (like friction and air resistance) do negative work on the roller - coaster cart, converting some of the mechanical energy into other forms of energy (such as heat and sound).

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QUESTION IMAGE

Question

Explanation:

Part A

Step1: Recall energy concepts

Step1: Recall potential energy formula

Step1: Analyze energy conversion from point 1 to 2

Answer:

Part B