Question

Based on the diagram of a roller coaster car on a roller coaster track, what statement is true?

A) The car at point A has more kinetic energy than the car at point C.
B) The car at point C has less kinetic energy than the car at point B.
C) The car at point C has more kinetic energy than the car at point B.
D) The car at point D has less potential energy than the car at point B.

Answer 1

Answer: The answer is C

A car at point B has more kinetic energy than the car at point D.

Kinetic energy is energy at work.

Potential energy is stored energy.

Answer 2

B) The car at point C has less kinetic energy than the car at point B.

Step-by-step explanation:

We have two types of energy involved in this situation:

- Gravitational potential energy: this is the energy related to the heigth of the car, and it is given by
`U=mgh`, where m is the mass of the car, g is the gravitational acceleration, and h is the heigth of the car. The potential energy is higher when the car is located higher above the ground.

- Kinetic energy: this is the energy due to the motion of the car, and it is given by
`K=(1)/(2)mv^2`, where m is the mass of the car and v is its speed. The kinetic energy is higher when the speed of the car is higher.

- The law of conservation of energy states that the total mechanical energy of the car (sum of potential energy and kinetic energy:
`E=U+K`) is constant). This implies that when the car is at a higher point, the kinetic energy is less (because U is larger, so K must be smaller), while when the car is at a lower point, the kinetic energy is larger.

- Based on what we have written so far, we can conclude that the correct statement is:

B) The car at point C has less kinetic energy than the car at point B.

Because the car at point C is located at a higher point than point B, so the car at point C has larger potential energy than at point B, which implies that car at point C has less kinetic energy than the car at point B.