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Standard XII

Physics

Work Done as Dot Product

A force F⃗=[y...

Question

A force $\to F = [y^i + x^j] N$ acts on a particle moving in $x - y$ plane starting from the point $(3, 5) m$ , the particle is taken along a straight line to $(5, 7) m$ . The work done by the force( in $J$ upto two decimals) is:

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Solution

Work done by variable force is
$W = \int \to F . (d x^i + d y^j)$
$W = [\int y d x + \int x d y] = \int d (x y)$
$W = \int_{(3, 5)}^{(5, 7)} d (x y) = 35 - 15 = 20 J$

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A force →F=[y^i+x^j]N acts on a particle moving in x−y plane starting from the point (3,5)m, the particle is taken along a straight line to (5,7)m. The work done by the force( in J upto two decimals) is:

Work done by variable force is W=∫→F.(dx^i+dy^j) W=[∫ydx+∫xdy]=∫d(xy) W=∫(5,7)(3,5)d(xy)=35−15=20 J

A force $\to F = [y^i + x^j] N$ acts on a particle moving in $x - y$ plane starting from the point $(3, 5) m$ , the particle is taken along a straight line to $(5, 7) m$ . The work done by the force( in $J$ upto two decimals) is:

Work done by variable force is
$W = \int \to F . (d x^i + d y^j)$
$W = [\int y d x + \int x d y] = \int d (x y)$
$W = \int_{(3, 5)}^{(5, 7)} d (x y) = 35 - 15 = 20 J$