A boy in a wheelchair (total mass, 47.0 kg ) wins a race...

A boy in a wheelchair (total mass, $47.0 \mathrm{~kg}$ ) wins a race with a skateboarder. He has a speed of $1.40 \mathrm{~m} / \mathrm{s}$ at the crest of a slope $2.60 \mathrm{~m}$ high and $12.4 \mathrm{~m}$ long. At the bottom of the slope, his speed is $6.20 \mathrm{~m} / \mathrm{s}$. If air resistance and rolling resistance can be modeled as a constant frictional force of $41.0 \mathrm{~N}$, find the work he did in pushing forward on his wheels during the downhill ride.

Key Concepts

Work-Energy Principle

This principle states that the net work done on an object is equal to its change in kinetic energy. It provides a framework to account for all forms of energy transfer in a system, making it particularly useful in problems where forces (both conservative and non-conservative) do work over a distance.

Gravitational Potential Energy

Gravitational potential energy is the energy stored in an object due to its height relative to a reference level. As an object moves downward in a gravitational field, this potential energy is converted into kinetic energy or is expended in overcoming resistive forces, which is key to analyzing energy transformations in motion on inclined planes.

Frictional Forces

Frictional forces are resistive forces that act opposite to the direction of motion, converting mechanical energy into thermal energy. They are non-conservative, meaning the work they do depends on the path taken, and must be accounted for when applying energy conservation principles in real-world scenarios.

Non-Conservative Work

Non-conservative work refers to energy changes caused by forces that do not conserve mechanical energy, such as friction or applied forces. Unlike conservative forces, the work done by non-conservative forces alters the total mechanical energy of a system, making it essential to include them when balancing energy transformations from potential to kinetic energy.

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