The Millennium Force is the highest roller coaster in North America. It reached a maximum height to 94.5 m. The total mass of the roller coaster car and its passengers is 1380 kg. The speed of the roller coaster is 41.1 m/s at its lowest point on the tracks. What is the efficiency of the roller coaster in transforming gravitational potential energy into kinetic energy?
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My Ek= 1165554.9J and my Ep= 1279322.1J
I got 9.11% as my answer. Is it correct?
Yes, your answer is correct.
Well, someone's got a head for numbers! Your answer of 9.11% efficiency is close, but just a bit off. Let's find out the correct answer and get this roller coaster on track!
To calculate the efficiency, we need to find the ratio of the kinetic energy (Ek) to the total energy input (Ep).
First, let's confirm the values you provided:
Ek = 1,165,554.9 J
Ep = 1,279,322.1 J
Now, divide the kinetic energy by the total energy input and multiply by 100 to convert it to a percentage:
Efficiency = (Ek / Ep) * 100
Plugging in the numbers, we get:
Efficiency = (1,165,554.9 J / 1,279,322.1 J) * 100
After some calculating, the correct efficiency comes out to be approximately 91.07%. So, the roller coaster is 91.07% efficient in transforming gravitational potential energy into kinetic energy!
Great work on your initial answer! Just a small miscalculation, but you were almost there. Keep up the good work!
To calculate the efficiency of the roller coaster in transforming gravitational potential energy into kinetic energy, we need to find the total energy input (gravitational potential energy) and the total energy output (kinetic energy).
Step 1: Calculate the gravitational potential energy (Ep) at the highest point:
Ep = mgh
Ep = (1380 kg) * (9.8 m/s^2) * (94.5 m)
Ep = 1,280,430 J
Step 2: Calculate the kinetic energy (Ek) at the lowest point:
Ek = 1/2 * mv^2
Ek = 1/2 * (1380 kg) * (41.1 m/s)^2
Ek = 1,659,134.845 J
Step 3: Calculate the efficiency:
Efficiency = (Energy Output / Energy Input) * 100%
Efficiency = (Ek / Ep) * 100%
Efficiency = (1,659,134.845 J / 1,280,430 J) * 100%
Efficiency = 129.5928956313%
Efficiency ≈ 130%
Thus, the correct efficiency of the roller coaster's transformation of gravitational potential energy into kinetic energy is approximately 130%, not 9.11%.
To calculate the efficiency of the roller coaster in transforming gravitational potential energy into kinetic energy, you need to calculate both the initial potential energy and the final kinetic energy.
First, let's calculate the initial potential energy (Ep). The formula for potential energy is:
Ep = m * g * h
Where:
m = mass (in kg)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height (in meters)
Given:
mass (m) = 1380 kg
height (h) = 94.5 m
Substituting the given values:
Ep = 1380 kg * 9.8 m/s^2 * 94.5 m
Ep = 1279322.1 J
Now, let's calculate the final kinetic energy (Ek). The formula for kinetic energy is:
Ek = 0.5 * m * v^2
Where:
m = mass (in kg)
v = velocity (in m/s)
Given:
mass (m) = 1380 kg
velocity (v) = 41.1 m/s
Substituting the given values:
Ek = 0.5 * 1380 kg * (41.1 m/s)^2
Ek = 1165554.9 J
Now that we have the initial potential energy (Ep) and the final kinetic energy (Ek), we can calculate the efficiency.
Efficiency = (Ek / Ep) * 100%
Substituting the calculated values:
Efficiency = (1165554.9 J / 1279322.1 J) * 100%
Efficiency = 0.9104 * 100%
Efficiency = 91.04%
Therefore, the efficiency of the roller coaster in transforming gravitational potential energy into kinetic energy is approximately 91.04%.
So, your answer of 9.11% is not correct. The correct answer is approximately 91.04%.