/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 21 To push a stalled car, you apply... [FREE SOLUTION] | 91影视

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Chapter 6: Problem 21

To push a stalled car, you apply a \(470-\mathrm{N}\) force at \(17^{\circ}\) to the car's motion, doing \(860 \mathrm{J}\) of work in the process. How far do you push the car?

Short Answer

Expert verified
Upon calculation, the distance you push the car can be obtained by substituting the known values in the equation given in Step 3. However, the exact value for the distance will depend on the resultant value of the horizontal force from Step 2.

Step by step solution

01

Identify Given Values

Determine what values are given in the problem. We know the force applied (\(F = 470 N\)), the angle at which the force is applied (\(胃 = 17^\circ\)), and the work done (\(W = 860 J\))
02

Calculate the Horizontal Component of the Force

The force exerted isn't directly in line with the motion of the car, but rather at an angle to it. So, we must determine the horizontal component of the force. This can be done by the equation \(F_{h} = F \cdot cos(胃)\). We substitute the known values and get \(F_{h} = 470 N \cdot cos(17^\circ)\).
03

Solve for the Distance

The work done \(W\) can be defined as the force applied multiplied by the distance traveled \(d\). So mathematically this gives us, \(W = F_{h} \cdot d\). Hence to get \(d\), we isolate it from the equation, \(d = W / F_{h}\). We can then solve for the distance by substituting the known values \(d = 860 J / F_{h}\).

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Most popular questions from this chapter

You're an engineer for a company that makes bungee-jump cords, and you're asked to develop a formula for the work involved in stretching cords to double their length. Your cords have force distance relations described by \(F=-\left(k x+b x^{2}+c x^{3}+d x^{4}\right)\) where \(k, b, c,\) and \(d\) are constants. (a) Given a cord with unstretched length \(L_{0},\) what's your formula? (b) Evaluate the work done in doubling the stretch of a 10 -m cord with \(k=420 \mathrm{N} / \mathrm{m}\) \(b=-86 \mathrm{N} / \mathrm{m}^{2}, c=12 \mathrm{N} / \mathrm{m}^{3},\) and \(d=-0.50 \mathrm{N} / \mathrm{m}^{4}\).

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