M3a energy pro 3 A small block with mass 7.4x10^-2kg is moving in the xy-plane.

Question

M3a energy pro 3 A small block with mass 7.4x10^-2kg is moving in the xy-plane. The net force on the block is described by the potential- energy function U(x,y) = (5.1J/m^2 )x^2-(3.82J/m^3) y^3. Part A What is the magnitude of the acceleration of the block when it is at the point x = 0.51m, Express your answer with the appropriate units. a = [m/s]^2 Part B What is the direction of the acceleration of the block when it is at the point x = 0.51m, y= 0.69m? Give the answer as an acute angle from the x axis. It should be the closest acute angle from the x axis and positive. Theta = degree from the x axis

Explanation / Answer

  x-component of force:
(Fx) = -?U/?x
(Fx) = -2(5.10)x
(Fx) = -10.2x

x-component of acceleration:
m(ax) = -10.2x
(0.074 kg)(ax) = -10.2(0.51 m)
(ax) = -70.29 m/s

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