Question

U = 1/2kh² + mgh Solve for h

A) h=1/2(2√(u-mgh))/k
B) h=(2√(u-mgh))/k
C) h=1/2√(u-mgh)/k
D) h=√(2(u-mgh))/k

Answer 1

To solve for h in the potential energy equation, U = 1/2kh² + mgh, subtract mgh from both sides, multiply by 2/k, and finally take the square root of both sides, giving the answer D) h=√(2(u-mgh))/k.

Step-by-step explanation:

The question at hand involves solving for the height, h, in the equation U = 1/2kh² + mgh, which pertains to potential energy in classical mechanics. To isolate h, you can follow these steps:

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• Subtract mgh from both sides of the equation to get 1/2kh² = U - mgh.
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• Multiply both sides of the equation by 2/k to eliminate the fraction and the factor of k associated with h², which gives h² = (2/k)(U - mgh).
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• Take the square root of both sides to solve for h, which results in h = √((2/k)(U - mgh)).

The correct option that matches this result is D) h=√(2(u-mgh))/k. This formula illustrates a concept commonly taught in high school physics courses. It's important to remember the steps taken to rearrange the equation and apply similar methods for solving quadratic equations in physics problems.