A 68 kg sky diver falls at a constant terminal speed of 59 m / s. (a) At what rate is the grav

step 1 So here, the 4 -Part A, the rate of change of the gravitational potential energy, we can say tha

A 68 kg sky diver falls at a constant terminal speed of 59...

A $68 \mathrm{~kg}$ sky diver falls at a constant terminal speed of $59 \mathrm{~m} / \mathrm{s}$. (a) At what rate is the gravitational potential energy of the Earth-sky diver system being reduced? (b) At what rate is the system's mechanical energy being reduced?

Key Concepts

Gravitational Potential Energy

Gravitational potential energy is the energy stored in an object due to its position in a gravitational field. In problems involving vertical motion, changes in this energy are given by the product of mass, gravitational acceleration, and change in height. When an object descends, its gravitational potential energy decreases at a rate proportional to its weight and the speed at which it is falling.

Terminal Velocity

Terminal velocity is the constant speed reached by an object when the force of gravity is balanced by the resistive force of drag. At terminal velocity, the net acceleration is zero, meaning the object’s kinetic energy remains constant even as it continues to lose gravitational potential energy. This balance is essential in understanding how energy is transformed and dissipated in the presence of non-conservative forces.

Mechanical Energy

Mechanical energy is the sum of an object's kinetic and potential energies. In systems where non-conservative forces like air resistance (drag) act, mechanical energy is not conserved because some of it is transformed into other forms of energy, such as thermal energy. In scenarios where the speed is constant, any decrease in potential energy is not converted into kinetic energy but is instead dissipated, thereby reducing the system’s total mechanical energy.

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