Questions: Question-7: As the skater is skating back and forth, the total energy of the skater is

Solution Steps

The total energy of a skater moving back and forth is the sum of their kinetic energy and potential energy. In a closed system, where no external forces like friction or air resistance are acting, the total mechanical energy remains constant. This is due to the conservation of energy principle.

1. Kinetic Energy (KE): This is the energy due to the skater's motion and is given by the formula: \[ KE = \frac{1}{2}mv^2 \] where \( m \) is the mass of the skater and \( v \) is their velocity.

2. Potential Energy (PE): This is the energy due to the skater's position, often related to height in a gravitational field. It is given by: \[ PE = mgh \] where \( m \) is the mass, \( g \) is the acceleration due to gravity, and \( h \) is the height above a reference point.

As the skater moves back and forth, their kinetic and potential energy will interchange. At the highest point of their motion, the potential energy is maximized, and kinetic energy is minimized. Conversely, at the lowest point, kinetic energy is maximized, and potential energy is minimized. However, the sum of kinetic and potential energy, which is the total energy, remains constant if no external work is done on the system.

Final Answer