A cyclist is coasting at 12 m / s when she starts down a 450-m-long slope that is 30 m high. The

step 1 Hi friends, this is a problem based on concept of conservation of mechanical energy. In this pro

A cyclist is coasting at 12 m / s when she starts down a...

A cyclist is coasting at $12 \mathrm{m} / \mathrm{s}$ when she starts down a $450-\mathrm{m}-\mathrm{long}$ slope that is $30 \mathrm{m}$ high. The cyclist and her bicycle have a combined mass of $70 \mathrm{kg}$. A steady $12 \mathrm{N}$ drag force due to air resistance acts on her as she coasts all the way to the bottom. What is her speed at the bottom of the slope?

Key Concepts

Work-Energy Theorem

The work-energy theorem links the net work done on an object to its change in kinetic energy. It accounts for both conservative and non-conservative forces, providing a framework to analyze the energy transformations and losses that occur in a mechanical system.

Conservation of Energy

This concept states that the total energy in a closed system remains constant as it transforms from one form to another. In mechanics, energy conservation involves converting potential energy to kinetic energy while accounting for energy losses due to non-conservative forces.

Gravitational Potential Energy

Gravitational potential energy is the energy stored in an object due to its position in a gravitational field. It depends on the object's mass, the gravitational acceleration, and the height above a reference level, and it converts into kinetic energy as the object moves downward.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion. It is proportional to the mass of the object and the square of its velocity. As potential energy converts during motion, its increase in velocity is reflected as an increase in kinetic energy.

Work Done by Non-Conservative Forces

Non-conservative forces, such as friction or air resistance, do work that converts mechanical energy into other forms like heat, which is not recoverable as mechanical energy. This work results in energy loss from the system, modifying the energy balance and final speed outcomes.

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