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An object is displaced from point A(2m,...

An object is displaced from point `A(2m,3m,4m)` to a point `B(1 m,2 m,3 m)` under a constant force ` F=(2hati + 3hatj + 4hatk)N`. Find the work done by this force in this process.

Text Solution

Verified by Experts

`W=int_(r_i)^(r_f) F*dr=int_((2m, 3m, 4,))^((1m, 2m, 3m,))(2hati + 3hatk + 4hatk)*(dxhati + dyhatj + dzhatk)`
`=[2x + 3y + 4z] _((2m, 3m, 4m)) ^((1m, 2m, 3m,))=-9J`
Alrernate Solution
Since, `F = "constant"`, we can also use.
`W=F*S`
Here, `S=r_f-r_i=(hati+2hatj+3hatj+3hatk)-(2hati+3hatj+4hatk)`
`=(-hati-hatj-hatk)`
`W=(2hati+3hatj+4hatk)*(-hati-hatj-hatk)`ltbrge-2-3-4=-9J`.
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