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Nonconservative forces are those that do not conserve mechanical energy in a system. They include forces like friction or external pushes and pulls that add or remove energy in forms other than potential and kinetic. For the skateboarder, two significant nonconservative forces are at play: the work done by the skateboarder himself, and the friction force between the skateboard and the ground.

• Positive Work by Skater: The skateboarder does positive work to increase his speed. Here, he's adding energy to the system, quantified as +80.0 J.
• Negative Work by Friction: Friction works in the opposite direction, reducing the overall mechanical energy of the system by -265 J.

These forces impact how kinetic energy changes, as energy is neither created nor destroyed but transformed and transferred between forms. Therefore, understanding the shift in energy through nonconservative forces is key to solving problems involving work-energy principles.

The concept of potential energy change involves how the energy stored in the system shifts due to changes in position. In gravitational contexts, it is related to the vertical displacement of an object.Change in gravitational potential energy (\( \Delta PE \)) is calculated as the difference between the potential energy at two different positions. It is determined using the formula:d \( \Delta PE = \text{PE}_f - \text{PE}_0 \)
where

• \( \text{PE}_f \) is the final potential energy.
• \( \text{PE}_0 \) is the initial potential energy.

This change tells us how much energy is stored or released as an object moves from one height to another, which is crucial in understanding vertical motion and energy conversion in gravitational fields.In the skateboarder’s case, solving for potential energy change helps determine if he is higher or lower than where he started.

Kinetic energy is the energy an object possesses due to its motion. It depends on both the mass of the object and its velocity, calculated using the formula:\( KE = \frac{1}{2}mv^2 \).

• Initial Kinetic Energy: With a mass of 55.0 kg and a starting speed of 1.80 m/s, the initial kinetic energy can be calculated. It reflects the energy due to motion at the beginning of the problem.
• Final Kinetic Energy: As the skateboarder reaches a final speed of 6.00 m/s, the kinetic energy calculation at this point shows the energy due to motion at the final speed.
• Change in Kinetic Energy: Calculated as the difference between the final and initial kinetic energies.

Understanding kinetic energy is fundamental in analyzing how work done by various forces affects an object's motion. The difference between initial and final kinetic energies represents the total work done by both nonconservative forces acting on the system.

Gravitational potential energy describes the energy an object stores due to its vertical position in a gravitational field. It is dependent on the mass of the object, gravity, and the height above a reference point.The formula for gravitational potential energy is given by:\( PE = mgh \)where:

• \( m \) is the mass of the object.
• \( g \) is the acceleration due to gravity (usually \( 9.8 \, \text{m/s}^2 \)).
• \( h \) is the height above the reference point.

In scenarios where both kinetic and potential energies are involved, understanding gravitational potential energy enables prediction of how an object will move vertically. For the skateboarder, analyzing how his vertical height changes help determine if he's spending or gaining this specific type of energy as he moves.