Question

1. The first, or lift, hill of the roller coaster gives it its maximum gravitational potential energy. What does this energy depend on? Howis it calculated?2. After the coaster starts down the first hill, how can its kinetic energy at any given point be calculated?3. As the kinetic and potential energy of the moving roller coaster change, what happens to the sum of the kinetic and potentialenergy? Why?4. In the real world, a roller coaster loses some of its energy to the environment. What might be some reasons that energy is lost?

Answer 1

1.

The gravitational potential energy depends on the height of the location of an object from the earth's surface. The important quantity is the position of an object.

The gravitational potential energy is calculated from the expression given as:

`U=\text{mgh}`

Here mass is taken as m, the acceleration due to gravity is taken as g, and the position of an object is taken as h.

2.

The kinetic energy mainly depends on the velocity of an object. The kinetic energy is calculated from the expression given as follows:

`K=(1)/(2)mv^2`

3.

The potential energy is maximum at the top of the hill, and minimum at the bottom while the kinetic energy starts increasing as the object descends down the hill. The potential energy is converted into kinetic energy.

This conversion from one form of energy to another form is due to the conservation of energy. From the energy conservation principle, the summation of the kinetic energy and potential energy remains constant.

4.

In the real world, a roller coaster loses some of its energy to the environment. The heat energy is lost to the environment.

It is due to the friction present between the roller and surface that is responsible for the generation of heat, which is lost to the environment.