NEET Class neet Answered

If U(xyz)= (xy+yz+zx), then find force act on particle at point (1m, -1m, 2m).

Asked by patra04011965 | 08 Oct, 2019, 07:29: PM

Expert Answer

Potential energy function, U(x,y,z) = ( x y + y z + z x ) ...............(1)

Force = - ∂U/∂r = - ( ∂U/∂x )

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- ( ∂U/∂y )

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- ( ∂U/∂z )

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.....................(2)

where

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and

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are unit vectors along x, y and z direction.

∂U/∂x = y + z ; ∂U/∂y = z + x ; ∂U/∂z = x + y

Hence force from eqn.(2), Force = - (y+z)

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- (z+x)

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- (x+y)

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....................(3)

Force at ( 1 m , -1 m , 2 m ) is given by, - (-1+2)

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- ( 2 + 1)

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- (1 -1)

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= -

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- 3

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....................(4)

magnitude of force = ( 1² + 3² )^1/2 = 3.16 N

direction of force is such that force vector makes 72ºangle with -ve x-axis

Answered by Thiyagarajan K | 08 Oct, 2019, 11:21: PM

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