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Chapter 9: Q. 78 (page 622)

Work

Find the work done by a force of 1newton acting in the direction 2i+2j+kin moving an object 3 meters from (0,0,0)to(1,2,2).

Short Answer

Expert verified

The work done is10Nm

Step by step solution

01

Step 1. Given information

A force of one newton is given in the direction2i+2j+kfrom(0,0,0)to(1,2,2)

02

Step 2. Finding force vector

First we need to find the vector of force as,

F鈫�=F.u^

Where Fis magnitude of force and u^is unit vector given by u^=u鈫�|u|

u=22+22+12=9=3

Therefore,

F鈫�=323i+23j+13k

03

Step 3. Finding work

Now take dot product of force vector and distance vector,

W=F路AB鈫�鈬�AB鈫�=(1i+2j+2k)=323i+23j+13k路(1i+2j+2k)=323路2+23路2+13路2=34+4+23=10Nm

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