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, 19:29: PM
Expert Answer
Potential energy function, U(x,y,z) = ( x y + y z + z x ) ...............(1)
Force = - ∂U/∂r = - ( ∂U/∂x ) - ( ∂U/∂y ) - ( ∂U/∂z ) .....................(2)
where , and 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) - (z+x) - (x+y) ....................(3)
Force at ( 1 m , -1 m , 2 m ) is given by, - (-1+2) - ( 2 + 1) - (1 -1) = - - 3 ....................(4)
magnitude of force = ( 12 + 32 )1/2 = 3.16 N
direction of force is such that force vector makes 72º angle with -ve x-axis
Answered by Thiyagarajan K | 08 Oct, 2019, 23:21: PM
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