Challenge: Roller Coaster Energy Analysis
You are about to model the motion of a roller coaster and analyze its energy transformations as it moves along a track. In this challenge, you will calculate the kinetic and potential energy at various positions, and visualize how energy is conserved throughout the ride. This task will help you see how physics principles like conservation of energy play out in a real-world scenario, reinforcing your understanding of kinetic and potential energy from the previous chapters.
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Model and analyze the energy transformations of a roller coaster as it moves along a track by following these steps:
- Use the provided
mass,heights, andvelocitiesarrays to represent the roller coaster at different positions along the track; - For each position, calculate the potential energy using the formula:
potential_energy = mass * g * height, wheregis the gravitational acceleration (defaultg = 9.81 m/s^2); - For each position, calculate the kinetic energy using the formula:
kinetic_energy = 0.5 * mass * velocity ** 2; - Calculate the total mechanical energy at each position by summing the potential and kinetic energy:
total_energy = potential_energy + kinetic_energy; - Store all energy values as NumPy arrays for efficient, element-wise calculations;
- Plot the potential energy, kinetic energy, and total mechanical energy as separate lines on the same graph, with track position (array index) on the x-axis and energy (in Joules) on the y-axis;
- Include axis labels, a legend, and a title on your plot for clarity;
- Use the provided sample data for demonstration and ensure your function returns the three calculated NumPy arrays: potential energy, kinetic energy, and total energy.
Hints:
- Use NumPy to efficiently perform calculations on arrays;
- Use Matplotlib to create the plot and clearly label each energy type.
Solution
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Completion rate improved to 4.76Challenge: Roller Coaster Energy Analysis
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You are about to model the motion of a roller coaster and analyze its energy transformations as it moves along a track. In this challenge, you will calculate the kinetic and potential energy at various positions, and visualize how energy is conserved throughout the ride. This task will help you see how physics principles like conservation of energy play out in a real-world scenario, reinforcing your understanding of kinetic and potential energy from the previous chapters.
Swipe to start coding
Model and analyze the energy transformations of a roller coaster as it moves along a track by following these steps:
- Use the provided
mass,heights, andvelocitiesarrays to represent the roller coaster at different positions along the track; - For each position, calculate the potential energy using the formula:
potential_energy = mass * g * height, wheregis the gravitational acceleration (defaultg = 9.81 m/s^2); - For each position, calculate the kinetic energy using the formula:
kinetic_energy = 0.5 * mass * velocity ** 2; - Calculate the total mechanical energy at each position by summing the potential and kinetic energy:
total_energy = potential_energy + kinetic_energy; - Store all energy values as NumPy arrays for efficient, element-wise calculations;
- Plot the potential energy, kinetic energy, and total mechanical energy as separate lines on the same graph, with track position (array index) on the x-axis and energy (in Joules) on the y-axis;
- Include axis labels, a legend, and a title on your plot for clarity;
- Use the provided sample data for demonstration and ensure your function returns the three calculated NumPy arrays: potential energy, kinetic energy, and total energy.
Hints:
- Use NumPy to efficiently perform calculations on arrays;
- Use Matplotlib to create the plot and clearly label each energy type.
Solution
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