A roller coaster cart of mass m = 201 kg starts stationary at point A, where h1 = 27.7 m and a while later is at B, where h2 = 7.1 m.
The acceleration of gravity is 9.8 m/s
2.
What is the potential energy of the cart
relative to the ground at A?
Answer in units of J.
(201*27.7*9.8)-(201*7.1*9.8)=40577.88J What did I do wrong
They are asking for the PE at A only:
PE = m*g*h1
It seems like you have made a mistake in calculating the potential energy. The correct formula for calculating the potential energy is P.E. = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
The potential energy at point A can be calculated as follows:
P.E. = mgh1 = (201 kg)(9.8 m/s^2)(27.7 m)
Evaluating this expression gives:
P.E. = 55532.86 J
So, the correct potential energy of the cart relative to the ground at point A is 55532.86 J.
Your calculation appears to be incorrect. Let's break down the correct calculation step by step.
The potential energy of an object at a certain height is determined by its mass, the acceleration due to gravity, and the height above the reference point.
To calculate the potential energy (PE) of the cart relative to the ground at point A, you can use the formula:
PE = m * g * h
Where:
m = mass of the cart (201 kg)
g = acceleration due to gravity (9.8 m/s^2)
h = height above the reference point (27.7 m)
Substituting the given values into the formula:
PE = 201 kg * 9.8 m/s^2 * 27.7 m
Now, let's calculate the potential energy:
PE = 55686.6 J
So, the correct potential energy of the cart relative to the ground at point A is 55686.6 Joules (J).