91Ó°ÊÓ

Potential energy, often abbreviated as PE, is the stored energy in an object due to its position or configuration. For a diver on a high tower, this energy is in the form of gravitational potential energy. It depends on three factors:

• Mass (\( m \)): The amount of matter in the diver's body.
• Gravitational acceleration (\( g \)): A constant \( 9.8 \, \text{m/s}^2 \), which is the rate at which gravity accelerates objects downward.
• Height (\( h \)): The vertical distance above the water.

The formula used to calculate potential energy is \( PE = mgh \).
For the diver, this calculation turns into \( PE = 67.0 \times 9.8 \times 3.00 \), giving us \( 1968.6 \) joules just before entering the water.
The concept of potential energy helps us understand the energy transformation that occurs as the diver falls. As she descends, this stored energy begins to change into kinetic energy.

Kinetic energy describes the energy an object has due to its motion. Once the diver leaps from the tower, her potential energy is converted into kinetic energy as she accelerates towards the water.
Just before hitting the water, all her initial potential energy is transformed into kinetic energy. This is because energy conservation implies that no energy is lost or gained, merely transformed from one form to another.
We use the same value calculated for potential energy to represent her kinetic energy right before impact: \( KE = 1968.6 \, \text{J} \).
This kinetic energy explains the power and speed with which the diver enters the water, illustrating a fundamental principle: what goes up, must come down, and the energy does not disappear during this process.

Nonconservative forces are forces that depend on the path taken and involve energy dissipation, such as friction or air resistance. In the case of the diver, the water's resistance as she penetrates the surface acts as a nonconservative force.
These forces take kinetic energy out of the diver, causing her to decelerate until she comes to a stop underwater. This energy is transformed rather than conserved, and cannot be described by only the initial and final states of motion.
The water force functioned here in dissipating the diver's kinetic energy into heat and sound as she slows from her initial speed to zero.

• Unlike gravity, which is conservative, water resistance is nonconservative because the energy is not stored for reuse.
• The Work-Energy Principle relates here, showing that the work done by a nonconservative force equals the change in kinetic energy, which was zero when the diver stopped.

The average force is a concept used to describe a constant force that yields the same energy change as the actual variable force over a distance. We determine this force during instances like a diver slowing in water due to nonconservative forces.
Following the Work-Energy Principle, the work done by the water \( (W) \) is equivalent to the diver's kinetic energy just before hitting the water: \( 1968.6 \, \text{J} \).

• Distance (\( d \)) over which this force acts is \( 1.10 \, \text{m} \)
• The formula for calculating average force is \( F_{average} = \frac{W}{d} \)
• Substituting the values: \( F_{average} = \frac{1968.6}{1.10} = 1789.64 \, \text{N} \)

This average force provides insight into the force exerted by the water against the diver, acting over the distance taken to bring her motion to rest.