Question

The motion of roller coasters depends upon the conversion of potential and kinetic energy. A 100-kg car starts from rest at the top of a hill with a height of 50 m. Which of the following is this car's kinetic energy at the bottom of the hill?

Answer 1

K=49,000 Joule

Step-by-step explanation:

Kinetic and Gravitational Potential Energy

The principle of conservation of the mechanical energy states that the mechanical energy of a system of particles remains unaltered unless some external non-conservative forces acting on the system.

The total mechanical energy present in the roller coasters is the sum of their kinetic and gravitational potential energies:

`\displaystyle ME=(m.v^2)/(2)+m.g.h`

If the roller coaster decreases its height, the speed will increase and compensates for the loss of potential energy. If the roller coaster increases its height, it will go slower and eventually stop until running out of kinetic energy.

We know the car starts from rest at the top of the hill of 50 m. This implies that the mechanical energy is

`\displaystyle ME=(100.0^2)/(2)+100.(9.8).(50)=49,000\ J`

When it reaches the bottom of the hill, the potential energy is zero, thus the car has only kinetic energy.

Kinetic energy at the bottom = 49,000 Joule