Question

A roller-coaster car has a potential energy of 400,000 j (400 kj) and a kinetic energy of 130,000 j (130 kj) at point a in its travel. At the low point of the ride, the potential energy is zero, and 60,000 j (60 kj) of work has been done against friction since it left point a. What is the kinetic energy of the roller coaster at this low point (in kj)?

Answer 1

The kinetic energy of the roller coaster at the low point is 470 kJ, after accounting for the loss of mechanical energy due to friction.

Step-by-step explanation:

The student's question refers to the conservation of mechanical energy in the context of a roller coaster's motion. The roller coaster has a total mechanical energy at point A, which is the sum of its potential energy (PE) and kinetic energy (KE). The problem tells us that the roller coaster has 400 kilojoules (kJ) of PE and 130 kJ of KE at point A, adding up to 530 kJ of total mechanical energy. As the roller coaster descends to the low point, it loses potential energy, which is converted into kinetic energy. However, we must also account for the work done against friction, which represents a loss of mechanical energy.

To find the kinetic energy at the low point, we subtract the work done against friction from the total mechanical energy at point A:

Total mechanical energy at point A = PE + KE = 400 kJ + 130 kJ = 530 kJ
Work done against friction = 60 kJ
Kinetic energy at the low point = Total mechanical energy at point A - Work done against friction = 530 kJ - 60 kJ = 470 kJ.