Calculate A) the conservative force described by the potential energy function U(x,y,z) = ½ k (2x³ +5y² - 3z¹) and B) the force function (in standard vector form) at (x, y, z) = (2, 3, 1) assuming that k = 1.5.
Calculate A) the conservative force described by the potential energy function U(x,y,z) = ½ k (2x³ +5y² - 3z¹) and B) the force function (in standard vector form) at (x, y, z) = (2, 3, 1) assuming that k = 1.5.
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![**Problem Statement:**
Calculate:
A) The conservative force described by the potential energy function
\[ U(x,y,z) = \frac{1}{2} k (2x^3 + 5y^2 - 3z^4) \]
B) The force function (in standard vector form) at \((x, y, z) = (2, 3, 1)\) assuming that \(k = 1.5\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3738e16a-10fd-4378-b4a3-b8733d2d5bb5%2F05ad939f-a686-4d06-8a5b-90f58b187751%2Fh4j2d8t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Calculate:
A) The conservative force described by the potential energy function
\[ U(x,y,z) = \frac{1}{2} k (2x^3 + 5y^2 - 3z^4) \]
B) The force function (in standard vector form) at \((x, y, z) = (2, 3, 1)\) assuming that \(k = 1.5\).
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