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A particle has shifted along some trajec...

A particle has shifted along some trajectory in the plane `xy` from point 1 whose radius vector `r_1=i+2j` to point 2 with the radius vector `r_2=2i-3j`. During that time the particle experienced the action of certain forces, one of which being `F=3i+4j`. Find the work performed by the force F. (Here `r_1`, `r_2`, and F are given in SI units).

Text Solution

Verified by Experts

As `vecF` is constant so the sought work done
`A=vecF*vecr=vecF*(vecr_2-vecr_1)`
or, `A=(3veci+4vecj)*[(2veci-3vecj)-(veci+2vecj)]=(3veci+4vecj)*(veci-5vecj)=17J`
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Knowledge Check

  • A force F = 2i+j-k acts as a point A whose position vector is 2i-j . IF point of application of F moves from the point A to the point B with P.V. 2i+j , then the work done by F is

    A
    4
    B
    20
    C
    2
    D
    none

  • A force F=Ai+Bj is applied to a point whose radius vector relative to the origin of coordinates O is equal to r=ai+bj , where a, b, A, B are constants, and i,j are the unit vectors of the x and y axes. Find the moment N and the arm l of the force F relative to the point O.

    A
    `(aB-Ab)/(sqrt(A^2+B^2))`
    B
    `(aA-Bb)/(sqrt(A^2+B^2))`
    C
    `(aB+Ab)/(sqrt(A^2+B^2))`
    D
    `(Ab-aB)/(sqrt(A^2+B^2))`

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