A 1 x10^3 kg roller coaster car is initially at the top of a rise, at point A. It then moves 50 m at an angle of 40 degrees below the horizontal to a lower point, B. (a) Choosing point B as the zero level of gravitational potential energy, find the potential energy of the car at A and B, and the difference in potential energy between these points. (b) Repeat part (a), choosing point A as the zero reference level.
To solve this problem, we need to use the formula for gravitational potential energy:
Potential Energy (PE) = mass (m) x gravitational acceleration (g) x height (h)
(a) Choosing point B as the zero level of gravitational potential energy:
1. Calculate the potential energy at point A:
PE at A = 1 x 10^3 kg x 9.8 m/s^2 x height at A
Since the roller coaster car is at the top of the rise at point A, the height at A would be the highest point of the roller coaster. Let's assume it is H meters.
PE at A = 1 x 10^3 kg x 9.8 m/s^2 x H
2. Calculate the potential energy at point B:
PE at B = 1 x 10^3 kg x 9.8 m/s^2 x height at B
To find the height at B, we can use trigonometry. The distance traveled horizontally is 50 m, and the angle with the horizontal is 40 degrees. We can calculate the height at B using the sine function:
height at B = 50 m x sin(40 degrees)
PE at B = 1 x 10^3 kg x 9.8 m/s^2 x (50 m x sin(40 degrees))
3. Calculate the difference in potential energy between points A and B:
Difference in PE = PE at B - PE at A
(b) Choosing point A as the zero level of gravitational potential energy:
1. Calculate the potential energy at point B:
PE at B = 0 (since it is chosen as the zero reference level)
2. Calculate the potential energy at point A:
PE at A = 1 x 10^3 kg x 9.8 m/s^2 x height at A
3. Calculate the difference in potential energy between points A and B:
Difference in PE = PE at A - PE at B
Note: Make sure to convert the angle from degrees to radians if required by the problem.