A 75.0-kg firefighter slides down a pole while a constant...

A $75.0-\mathrm{kg}$ firefighter slides down a pole while a constant frictional force of $900 \mathrm{~N}$ retards her motion. A horizon- tal $20.0-\mathrm{kg}$ platform is supported by a spring at the bottom of the pole to cushion the fall. The firefighter starts from rest $4.00 \mathrm{~m}$ above the platform, and the spring constant is $4000 \mathrm{~N} / \mathrm{m}$. Find (a) the firefighter's speed just before she collides with the platform and (b) the maximum distance the spring is compressed. (Assume the frictional force acts during the entire motion.)

A $75.0-\mathrm{kg}$ firefighter slides down a pole while a constant frictional force of $900 \mathrm{~N}$ retards her motion. A horizon-
tal $20.0-\mathrm{kg}$ platform is supported by a spring at the bottom of the pole to cushion the fall. The firefighter starts from rest $4.00 \mathrm{~m}$ above the platform, and the spring constant is $4000 \mathrm{~N} / \mathrm{m}$. Find (a) the firefighter's speed just before she collides with the platform and (b) the maximum distance the spring is compressed. (Assume the frictional force acts during the entire motion.)

Key Concepts

Elastic Potential Energy and Hooke’s Law

Elastic potential energy is the energy stored in elastic materials or systems, such as springs, when they are compressed or stretched, and is calculated using the formula (1/2)kx², where k is the spring constant and x is the displacement. Hooke’s Law, which states that the force exerted by a spring is proportional to its compression or elongation, is essential for understanding how the spring cushions a fall.

Kinetic Energy

Kinetic energy is the energy of motion possessed by an object, given by the expression (1/2)mv². It is an important concept in problems involving motion, as it often results from the conversion of potential energy, and includes the analysis of speeds prior to collision or impact.

Work Done by Friction

Work done by friction represents the energy lost from the system due to the frictional force acting opposite to the direction of motion. It is computed as the product of the frictional force and the distance over which it acts, and it directly reduces the mechanical energy available for conversion into kinetic or other forms of energy.

Conservation of Energy with Non-Conservative Forces

This concept involves accounting for the total mechanical energy (kinetic plus potential energy) in a system while recognizing that non-conservative forces, such as friction, perform work that reduces the system’s mechanical energy. It is used to analyze scenarios where energy is transformed into different forms or dissipated as heat.

Gravitational Potential Energy

Gravitational potential energy is the energy stored by an object due to its position in a gravitational field, expressed as mgh, where m is mass, g is the acceleration due to gravity, and h is height. It is a central concept when analyzing energy transformations in vertical motion.

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