1) A particle has an potential energy function described by U(x) = x2 +y2 +Z2-2x

Question

1) A particle has an potential energy function described by U(x) = x2 +y2 +Z2-2xyz. Determine the force on the particle at the coordinates (-2,1,3) 2) A 20 kg projectile is fired with a velocity of 500 m/s directed at an angle of 30° above the horizontal. What is the velocity (vector) of the projectile when it is halfway to its maximum height? [Use energy conservation to solve this problem.] 3) The potential energy of a point particle is given by the equation U(x) = x3-3x + 2. points? (Show your work)

Explanation / Answer

Answer A

F = Fx i + Fy j + Fz k

and as we know

Fx = dU / dx , Fy = dU/dy , Fz = dU/dz

so,

Fx = d / dx (x2+ y 2 + z 2 2xyz)

Fx =2x - 2yz

Fy = d /dy (x2+ y 2 + z 2 2xyz)

Fy = 2y-2xz

same way

Fz = 2z-2xy

so putting the value we get

F = (2x-2yz)i + (2y-2xz) j+(2z-2xy)k

applying the co-ordinate value we get (-2, 1 , 3)

F = (2(-2) - 2*1*3)i + (2*1 -2*(-2)*3)j+(2*3-2*(-2)*1)k

F = (-10) i + 14j -10k

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so ask another questions as a saperate question

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