Question

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

Answer 1

Answer:

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

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 $K=\frac{1}{2}mv^2$, 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.