The kinetic energy of the roller coaster at the low point is 470 kJ, calculated by considering the initial total mechanical energy and subtracting the energy lost to friction, according to the law of conservation of energy.
To determine the kinetic energy of the roller coaster at the low point, we can use the law of conservation of energy. This law states that the total mechanical energy in an isolated system remains constant, provided there is no energy loss due to friction or other forces. In the absence of friction, the roller coaster's potential energy (PE) at the high point would convert entirely into kinetic energy (KE) at the low point. However, in this problem, work has been done against friction, reducing the total mechanical energy.
The initial total mechanical energy at point A is the sum of potential and kinetic energy, which is 400,000 J + 130,000 J = 530,000 J. At the low point, 60,000 J has been used to do work against friction, so the total mechanical energy would decrease to 530,000 J - 60,000 J = 470,000 J. Since the potential energy at the low point is zero, all of this energy is in the form of kinetic energy. Therefore, the kinetic energy at the low point is 470,000 J, or 470 kJ.