The potentil energy function of a paricle in a region of space is given as u={2x²+3y³+2z) here x y z in meter find the force acting on rhe particle p(1 2. 3)
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we know relation between force and potential energy is ----
Fx= -dU/dx
Fy= -dU/dy
Fz= -dU/dz
now Fx= -d (2x^2)/dx= -4x
Fx= -4 at x =1
Fy= -d (3y^3)/dy
= -9y^2 = -9 x 4 = -36 at y=2
Fz=d (2z)/dz=2
now F=Fx i+ Fy j + Fz k
= -4 i +(-36) j + 2k
Fx= -dU/dx
Fy= -dU/dy
Fz= -dU/dz
now Fx= -d (2x^2)/dx= -4x
Fx= -4 at x =1
Fy= -d (3y^3)/dy
= -9y^2 = -9 x 4 = -36 at y=2
Fz=d (2z)/dz=2
now F=Fx i+ Fy j + Fz k
= -4 i +(-36) j + 2k
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Easy question..... Don't panic about it
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