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Chapter 1: Problem 38

A mountain climber's oxygen tank contains 1 lb of oxygen when he begins his rip at sea level where the acceleration of gravity is $32.174 \mathrm{ft} / \mathrm{s}^{2}$. What is the weight of the oxygen in the tank when he reaches the top of Mt. Everest where the acceleration of gravity is $32.082 \mathrm{fts}^{2} ?$ Assume that no oxygen has been removed from the tank; it will be used on the descent portion of the climb.

Short Answer

Expert verified
The weight of the oxygen in the tank when the climber reaches the top of Mt. Everest is \(32.082 lb \cdot ft/s^2\).

Step by step solution

01

Identify Mass and Initial Gravity

The mass of the oxygen in the tank is given as 1 lb and the acceleration due to gravity at sea level is \(32.174 \, ft/s^2\).
02

Calculate Initial Weight

Since the weight equals the product of mass and gravity, the weight of the oxygen at sea level is \(1 lb \times 32.174 \, ft/s^2 = 32.174 \, lb \cdot ft/s^2\). This is done using the force equation \(F = m \cdot a\) where m is the mass and a is the acceleration due to gravity.
03

Identify Final Gravity

The acceleration due to gravity at the top of Mount Everest is given as \(32.082 ft/s^2\).
04

Calculate Final Weight

Again applying the formula for weight (mass x gravity), the weight of the oxygen at the top of Mount Everest is \(1 lb \times 32.082 ft/s^2 = 32.082 lb \cdot ft/s^2\).

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