Question

The constant forces F1 = 8 + 29 + 32 N and F2 = 48 - 59 - 22 N act together on a particle during a displacement from the point A (20, 15,0)m to the point B (0,07) m. What is the work done on the particle? The work done is given by F. f, where is the resultant force (here F = Fi + F2) and is the displacement.

Answer 1

- 600 J

Step-by-step explanation:

A (20, 15, 0 ) m

B (0, 0, 7) m

`\overrightarrow{F_(1)}=8\widehat{i}+29\widehat{j}+32\widehat{k}`

`\overrightarrow{F_(2)}=48\widehat{i}-59\widehat{j}-22\widehat{k}`

Net force

`\overrightarrow{F}=\overrightarrow{F_(1)}+\overrightarrow{F_(2)}`

`\overrightarrow{F}}=\left ( 8+48 \right )\widehat{i}+\left ( 29-59 \right )\widehat{j}+\left ( 32-22 \right )\widehat{k}`

`\overrightarrow{F}}=56\widehat{i}-30\widehat{j}+10\widehat{k}`

`\overrightarrow{S}=\overrightarrow{OB}-\overrightarrow{OA}`

`\overrightarrow{S}=\left ( 0-20 \right )\widehat{i}+\left ( 0-15 \right )\widehat{j}+\left ( 7-0 \right )\widehat{k}`

`\overrightarrow{S}=-20\widehat{i}-15\widehat{j}+7\widehat{k}`

Work done is defined as

`W = \overrightarrow{F}.\overrightarrow{S}`

`W = \left ( 56\widehat{i}-30\widehat{j}+10\widehat{k} \right ).\left (-20\widehat{i}-15\widehat{j}+7\widehat{k}  \right )`

W = -1120 + 450 + 70

W = - 600 J