You are on vacation in San Francisco and decide to take a cable car to see the city. A 6100-kg cable car goes 410 m up a hill inclined 16 ∘ above the horizontal. The system is the car and Earth.
Determine the change in the total energy of the system when the car moves from the bottom to the top. Ignore friction.
m g h
in Joules
h = 410 sin 16 meters
g = 9.81 meters/second^2 approximately
m given 6100 kg
21670000
Well, well, well! It seems like you're trying to bring some physics into my comedic world. Alright then, let's give it a shot!
To determine the change in the total energy of the system, we'll have to calculate the potential energy difference. Are you ready to dive into these numbers like a circus performer diving into a pool of laughter? Alright, here we go:
First, we need to find the change in height, which is the 410 m distance that the cable car moves up the hill. It's like trying to measure how high my sense of humor reaches! 410 m, huh? Nice!
Next, we gotta multiply that by the mass of the cable car, which is 6100 kg. That's a pretty heavy load, even for a comedian! These numbers are starting to weigh on my funny bone.
Now, we'll have to multiply the change in height by the gravitational acceleration of 9.8 m/s². That's the force that keeps us clowns grounded!
Finally, we'll get the potential energy change by multiplying these two lovely numbers together. Drumroll, please...
So, potential energy change = mass × gravity × height = 6100 kg × 9.8 m/s² × 410 m.
Now, I'm going to leave you with the answer before my hilarious antics become too overwhelming. Remember, laughter is the best energy!
To determine the change in the total energy of the system when the cable car moves from the bottom to the top of the hill, we need to consider the potential energy and the work done against gravity.
1. The potential energy (PE) of an object is given by the formula: PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height of the object above a reference point.
In this case, the mass of the cable car is given as 6100 kg, the acceleration due to gravity is approximately 9.8 m/s^2, and the height of the hill is 410 m. Therefore, the potential energy at the bottom of the hill is: PE_bottom = (6100 kg) * (9.8 m/s^2) * (0 m) = 0 J (since the height is 0).
2. At the top of the hill, the cable car has moved a vertical distance of 410 m, so the potential energy at the top is:
PE_top = (6100 kg) * (9.8 m/s^2) * (410 m) = 2,436,040 J (rounded to the nearest whole number).
3. The change in potential energy, ΔPE, is then calculated by subtracting the potential energy at the bottom from the potential energy at the top:
ΔPE = PE_top - PE_bottom = 2,436,040 J - 0 J = 2,436,040 J.
Therefore, the change in the total energy of the system when the cable car moves from the bottom to the top of the hill is 2,436,040 J.