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Three constant forces vecF1=2hati-3hatj+...

Three constant forces `vecF_1=2hati-3hatj+2hatk`, `vecF_2=hati+hatj-hatk`, and `vecF_3=3hati+hatj-2hatk` in newtons displace a particle from `(1, -1, 2)` to `(-1, -1, 3)` and then to `(2, 2, 0)` (displacement being measured in meters). Find the total work done by the forces.

Text Solution

Verified by Experts

Net (resultant) force, `vecF=vecF_1+vecF_2+vecF_3=6hati-hatj-hatkdyn`
and net displacement, `vecs=(2-1)hati+(2+1)hatj+(0-2)hatk`
`=hati+3hatj-2hatkm`
Therefore, work done,
`W=vecF.vecs=(6hati-hatj-hatk)*(hati+3hatj-2hatk)Nm`
`=(6-3+2)xx10^-5J=5xx10^-5J`
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