/*! 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 16 A body constrained to move in \(... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 16

A body constrained to move in \(y\)-direction is subjected to a force given by \(\vec{F}=(-2 \vec{i}+15 \vec{j}+6 \vec{k}) N\). The work done by this force in moving the body a distance of \(10 \mathrm{~m}\) along the \(y\)-axis is (A) \(20 \mathrm{~J}\) (B) \(150 \mathrm{~J}\) (C) \(60 \mathrm{~J}\) (D) \(190 \mathrm{~J}\)

Short Answer

Expert verified
The work done by the force in moving the body a distance of \(10m\) along the y-axis is calculated using the dot product of the force vector, \(\vec{F} = (-2\vec{i} + 15\vec{j} + 6\vec{k}) N\), and the displacement vector, \(\vec{d} = (0\vec{i} + 10\vec{j} + 0\vec{k}) m\). The dot product is \(\vec{F} \cdot \vec{d} = (-2)(0) + (15)(10) + (6)(0) = 150 J\). Therefore, the correct answer is \(150 \mathrm{~J}\).

Step by step solution

01

Write down the given force vector and displacement vector

In this problem, we are given that the force vector, \(\vec{F}\), acting on the body is given by: \[ \vec{F} = (-2\vec{i} + 15\vec{j} + 6\vec{k}) N \] We are also given that the body moves a distance of \(10m\) along the y-axis, so the displacement vector, \(\vec{d}\), is given by: \[ \vec{d} = (0\vec{i} + 10\vec{j} + 0\vec{k}) m \]
02

Calculate the dot product of the force vector and displacement vector

The work done by the force is given by the dot product of the force vector, \(\vec{F}\), and the displacement vector, \(\vec{d}\). The dot product of two vectors, \(\vec{A} = (A_x\vec{i} + A_y\vec{j} + A_z\vec{k})\) and \(\vec{B} = (B_x\vec{i} + B_y\vec{j} + B_z\vec{k})\), is given by: \[ \vec{A} \cdot \vec{B} = A_xB_x + A_yB_y + A_zB_z \] So the work done by the force is: \[ W = \vec{F} \cdot \vec{d} = (-2)(0) + (15)(10) + (6)(0) = 150 J \]
03

Identify the correct answer choice

The work done by the force in moving the body a distance of \(10m\) along the y-axis is \(150J\). Thus, the correct answer is option (B) \(150 \mathrm{~J}\).

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Most popular questions from this chapter

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