In this problem, we encounter potential energy and force. Thus, we know that it is a Force-Potential energy problem.

Force and potential are related by:

$\overline{){\mathbf{F}}{\mathbf{=}}\frac{\mathbf{d}\mathbf{U}}{\mathbf{d}\mathbf{y}}}$

Power rule of derivation:

$\overline{)\frac{\mathit{d}}{\mathit{d}\mathit{t}}\mathbf{\left(}{\mathit{x}}^{\mathit{n}}\mathbf{\right)}{\mathbf{=}}{\mathit{n}}{{\mathit{x}}}^{\mathit{n}\mathbf{-}\mathbf{1}}}$

**A)**

We'll calculate values of U for a range of values of y.

A particle moving along the y-axis has the potential energy U = 4y^{3} J, where y is in m.

A) Graph the potential energy from y = 0 m to y =2 m.

B) What is the y-component of the force on the particle at y = 0 m?

C) What is the y-component of the force on the particle at y = 1 m?

D )What is the y-component of the force on the particle at y = 2 m?

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