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Chapter 7: Problem 8

A tightrope walker follows an essentially horizontal rope between two mountain peaks of equal altitude. A climber descends from one peak and climbs the other. Compare the work done by the gravitational force on the tightrope walker and the climber.

Short Answer

Expert verified
The work done by the gravitational force on both the tightrope walker and the climber is zero.

Step by step solution

01

Understand the concept of work

The work done by a force, according to physics, is given as \(W = F \cdot d \cdot cosθ\), where \(F\) is the force, \(d\) is the distance, and \(θ\) is the angle between the direction of force and the direction of motion. The gravitational force acts vertically downwards while the movement of both individuals takes place along the direction of their respective paths.
02

Calculate work done for the tightrope walker

For the tightrope walker, the direction of movement is horizontal, meaning perpendicular to gravitational force, so the angle between them is 90 degrees. Since cosine of 90 degrees is 0, the work done by gravity on the tightrope walker, irrespective of the distance covered, will be 0 (since \(W = F \cdot d \cdot cos90\) and \(cos90 = 0\))
03

Calculate work done for the climber

Now for the climber, when he is descending, the direction of movement is in line with the gravitational force while on ascending, it is opposite the gravitational force. However, in both these cases, the magnitudes of the work done by gravity are equal and the total work done, therefore, comes out to be 0 (downhill work is negative and uphill work is positive, canceling each other out)

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Most popular questions from this chapter

A particle moves along the \(x\) -axis under the influence of a force \(F=a x^{2}+b,\) where \(a\) and \(b\) are constants. Find its potential energy as a function of position, taking \(U=0\) at \(x=0\)

A spring of constant \(k,\) compressed a distance \(x,\) is used to launch a mass \(m\) up a frictionless slope at angle \(\theta .\) Find an expression for the maximum distance along the slope that the mass moves after leaving the spring.

A \(60-\mathrm{kg}\) hiker ascending \(1250-\mathrm{m}\) -high Camel's Hump mountain in Vermont has potential energy \(-240 \mathrm{kJ} ;\) the zero of potential energy is taken at the mountaintop. What's her altitude?

The force exerted by an unusual spring when it's compressed a distance \(x\) from equilibrium is \(F=-k x-c x^{3},\) where \(k=220 \mathrm{N} / \mathrm{m}\) and \(c=3.1 \mathrm{N} / \mathrm{m}^{3} .\) Find the stored energy when it's been compressed \(15 \mathrm{cm}\)

If conservation of energy is a law of nature, why do we have programs- -like mileage requirements for cars or insulation stan- -dards for buildings- -designed to encourage energy conservation?
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