91Ó°ÊÓ

Kinetic energy is the energy an object possesses due to its motion. When an object is in motion, it has the capability to do work. This is encapsulated by the formula for kinetic energy:

• \[ KE = \frac{1}{2}mv^2 \]

where \( KE \) is the kinetic energy, \( m \) is the mass of the object, and \( v \) is its velocity.
In the context of the skeleton track exercise, when the sled moves down the track, the gravitational potential energy is converted into kinetic energy, increasing the speed of the sled.
Initially, at the top of the track, the kinetic energy is near zero because the sled's starting speed is negligible.
As it slides down, kinetic energy builds up due to the conversion of potential energy into kinetic energy under the influence of gravity.
At the bottom of the track, where the height is minimal, the kinetic energy is at its maximum if we assume no friction or air resistance is acting on the sled.

Potential energy refers to the stored energy of an object due to its position or state. In mechanical contexts like the skeleton sport example, we're often dealing with gravitational potential energy.
Gravitational potential energy is the energy held by an object because of its vertical position relative to a lower position, which can be calculated as:

• \[ PE = mgh \]

where \( PE \) is potential energy, \( m \) is mass, \( g \) is the acceleration due to gravity (approximately \(9.8 \text{m/s}^2\) on Earth), and \( h \) is the height.
In the skeleton run, the sled has maximum potential energy at the top of the track due to its elevated position. As the participant descends, this potential energy is transformed into kinetic energy as potential decreases while speed increases.

• This energy transformation follows the principle of conservation of energy in an ideal situation.
• If friction is ignored, all the potential energy converts into kinetic energy by the bottom of the track.

Work is a measure of energy transfer when a force is applied to an object causing it to move. It is calculated as the product of force and displacement in the direction of the force:

• \[ W = F \cdot d \cdot \cos(\theta) \]

However, when considering energy conservation, work can also be thought of as the energy transferred to or from an object by means of nonconservative forces like friction and air resistance.
In the skeleton scenario, these nonconservative forces are responsible for the difference between the ideal mechanical energy (with no losses) and the actual mechanical energy (with losses).
The work done by these nonconservative forces can be calculated as the difference between the ideal kinetic energy and the actual kinetic energy:

• \[ W_{nc} = KE_{actual} - KE_{ideal} \]

If \( W_{nc} \) is negative, it indicates that the forces like friction have done negative work, thus removing energy from the system.
In our scenario, the actual speed at the bottom is less than the calculated ideal speed which indicates energy has been transformed into heat and sound due to work done by friction and air resistance.