A 55.0-kg skateboarder starts out with a speed of 1.80 m / s. He does +80.0 J of work on himself

step 1 In this problem we have given the work done is equal to 80 jule and work done by the friction is

A 55.0-kg skateboarder starts out with a speed of 1.80 m /...

A 55.0-kg skateboarder starts out with a speed of 1.80 $\mathrm{m} / \mathrm{s}$. He does $+80.0 \mathrm{J}$ of work on himself by pushing with his feet against the ground. In addition, friction does -265 J of work on him. In both cases, the forces doing the work are nonconservative. The final speed of the skateboarder is $6.00 \mathrm{m} / \mathrm{s} .$ (a) Calculate the change $\left(\Delta \mathrm{PE}=\mathrm{PE}_{\mathrm{f}}-\mathrm{PE}_{0}\right)$ in the gravitational potential energy. (b) How much has the vertical height of the skater changed, and is the skater above or below the starting point?

Key Concepts

Work-Energy Theorem

The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. This principle is foundational in mechanics and allows us to account for the energy added or removed from a system by external forces, including both conservative and non-conservative forces.

Nonconservative Forces

Nonconservative forces, such as friction or an external push, do work that changes the total mechanical energy of a system. Unlike conservative forces where energy is stored and can be fully recovered, nonconservative forces dissipate energy (often as heat) or add energy, thereby affecting both kinetic and potential energy in the system.

Kinetic Energy

Kinetic energy is the energy associated with the motion of an object and is calculated using the formula (1/2)mv², where m is the mass and v is the velocity. Changes in speed directly influence kinetic energy, and the work done on the object manifests in changes in its kinetic energy as specified by the work-energy theorem.

Gravitational Potential Energy

Gravitational potential energy is the energy possessed by an object due to its position in a gravitational field, typically given by the product mgh, where m is mass, g is the acceleration due to gravity, and h is the height above a reference level. Changes in gravitational potential energy reflect vertical displacements and are crucial for understanding energy transformations when an object moves upward or downward.

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