A 1200-kg roller coaster car is initially at the top of a rise, at point circle a. It then moves 145 ft, at an angle of 40.0° below the horizontal, to a lower point circle b.
(a) Choose the car at point circle b to be the zero configuration for gravitational potential energy of the roller coaster−Earth system. Find the potential energy of the system when the car is at points circle a and circle b, and the change in potential energy as the coaster moves between these points.
at point circle a J
at point circle b J
change in potential energy J
(b) Repeat part (a), setting the zero configuration with the car at point circle a
at point circle a J
at point circle b J
change in potential energy J
adf
I used the gravitational potential formula and plugged in 1200 * 9.8 * 45.31
(a) To find the potential energy at points circle a and circle b, we can use the formula:
Potential energy = mass * acceleration due to gravity * height
Given:
Mass (m) = 1200 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Height at point circle a (h_a) = 0
Height at point circle b (h_b) = 145 ft = 44.2 m
(change in height, Δh = h_b - h_a = 44.2 - 0 = 44.2 m)
At point circle a:
Potential energy at point circle a = mass * acceleration due to gravity * height at point circle a
= 1200 kg * 9.8 m/s^2 * 0
= 0 J
At point circle b:
Potential energy at point circle b = mass * acceleration due to gravity * height at point circle b
= 1200 kg * 9.8 m/s^2 * 44.2 m
= 519,264 J
Change in potential energy = Potential energy at point circle b - Potential energy at point circle a
= 519,264 J - 0 J
= 519,264 J
Therefore, the potential energy at point circle a is 0 J, the potential energy at point circle b is 519,264 J, and the change in potential energy as the coaster moves between these points is 519,264 J.
(b) Setting the zero configuration with the car at point circle a means that the potential energy at point circle a is considered zero.
At point circle a:
Potential energy at point circle a = 0 J
At point circle b:
Potential energy at point circle b = mass * acceleration due to gravity * height at point circle b
= 1200 kg * 9.8 m/s^2 * 44.2 m
= 519,264 J
Change in potential energy = Potential energy at point circle b - Potential energy at point circle a
= 519,264 J - 0 J
= 519,264 J
Therefore, when the zero configuration is set with the car at point circle a, the potential energy at point circle a is 0 J, the potential energy at point circle b is 519,264 J, and the change in potential energy as the coaster moves between these points is 519,264 J.
To solve this problem, we need to calculate the potential energy at points A and B, as well as the change in potential energy between the two points.
(a) When the car is at point B, we choose this location as the zero configuration for gravitational potential energy. This means that the potential energy at point B is zero.
To find the potential energy at point A, we can use the formula for gravitational potential energy:
Potential energy = mass × acceleration due to gravity × height
Given data:
Mass of the car (m) = 1200 kg
Acceleration due to gravity (g) = 9.8 m/s²
Height (h) = distance from point B to point A = 145 ft
First, let's convert the height from feet to meters:
1 ft = 0.3048 m
Height (h) = 145 ft × 0.3048 m/ft = 44.196 m
Now, we can calculate the potential energy at point A:
Potential energy at point A = 1200 kg × 9.8 m/s² × 44.196 m = 514729.92 J
The potential energy at point B is zero.
The change in potential energy as the coaster moves from point A to point B is simply the difference between the potential energy at point B and the potential energy at point A:
Change in potential energy = Potential energy at point B - Potential energy at point A = 0 J - 514729.92 J = -514729.92 J
Therefore:
Potential energy at point A = 514729.92 J
Potential energy at point B = 0 J
Change in potential energy = -514729.92 J
(b) Now, let's set the zero configuration with the car at point A.
This means that the potential energy at point A is zero.
To find the potential energy at point B, we can use the same formula as before:
Potential energy = mass × acceleration due to gravity × height
Given data:
Mass of the car (m) = 1200 kg
Acceleration due to gravity (g) = 9.8 m/s²
Height (h) = distance from point A to point B = 145 ft
First, let's convert the height from feet to meters:
1 ft = 0.3048 m
Height (h) = 145 ft × 0.3048 m/ft = 44.196 m
Now, we can calculate the potential energy at point B:
Potential energy at point B = 1200 kg × 9.8 m/s² × 44.196 m = 514729.92 J
The potential energy at point A is zero.
The change in potential energy as the coaster moves from point A to point B is simply the difference between the potential energy at point B and the potential energy at point A:
Change in potential energy = Potential energy at point B - Potential energy at point A = 514729.92 J - 0 J = 514729.92 J
Therefore:
Potential energy at point A = 0 J
Potential energy at point B = 514729.92 J
Change in potential energy = 514729.92 J