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Chapter 9: Q. 33 (page 613)

Find the acute angle that a constant unit force vector makes with the positive x-axis if the work done by the force in moving a particle from 0,0to4,0equals2.

Short Answer

Expert verified

The acute angle that a constant unit force vector makes with the positive x-axis is伪=60鈭�.

Step by step solution

01

Step 1. Given Information

The work done is equal to 2when the particle is moving from 0,0to4,0.

We have to find the acute angle that a constant unit force vector makes with the positivex-axis.

02

Step 2. Finding an acute angle

As we know the work done by a constant force Fin moving an object from a point, Ato a point Bis defined as W=F路AB鈫�.

The particle is moving from A=0,0toB=4,0,so role="math" localid="1646831923394" AB鈫�=4i+0j

Now, the force factor F is

F=Fcos伪i+sin伪jF=cos伪i+sin伪jF=1

Let's put all the values in the formula of work done

W=F路AB鈫�2=cos伪i+sin伪j路4i+0j2=4cos伪12=cos伪伪=60鈭�

Thus, the acute angle is60掳.

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