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U=(1)/(2)kx^(2)
The elastic energy of an object, 
U, is determined by its absolute compression, 
x, and the spring constant of the object, 
k, as shown in the formula. Which of the following correctly shows the object's absolute compression in terms of its elastic energy and spring constant?
Choose 1 answer:
(A) 
x=sqrt((kU)/(2))
B 
x=sqrt((2U)/(k))
(C) 
x=(sqrt(2U))/(k)
(D) 
x=((2U)/(k))^(2)

U=12kx2 U=\frac{1}{2} k x^{2} \newlineThe elastic energy of an object, U U , is determined by its absolute compression, x x , and the spring constant of the object, k k , as shown in the formula. Which of the following correctly shows the object's absolute compression in terms of its elastic energy and spring constant?\newlineChoose 11 answer:\newline(A) x=kU2 x=\sqrt{\frac{k U}{2}} \newline(B) x=2Uk x=\sqrt{\frac{2 U}{k}} \newline(C) x=2Uk x=\frac{\sqrt{2 U}}{k} \newline(D) x=(2Uk)2 x=\left(\frac{2 U}{k}\right)^{2}

Full solution

Q. U=12kx2 U=\frac{1}{2} k x^{2} \newlineThe elastic energy of an object, U U , is determined by its absolute compression, x x , and the spring constant of the object, k k , as shown in the formula. Which of the following correctly shows the object's absolute compression in terms of its elastic energy and spring constant?\newlineChoose 11 answer:\newline(A) x=kU2 x=\sqrt{\frac{k U}{2}} \newline(B) x=2Uk x=\sqrt{\frac{2 U}{k}} \newline(C) x=2Uk x=\frac{\sqrt{2 U}}{k} \newline(D) x=(2Uk)2 x=\left(\frac{2 U}{k}\right)^{2}
  1. Multiply by 22: We have U=(12)kx2U = (\frac{1}{2})kx^2 and we need to solve for xx.
  2. Divide by kk: First, multiply both sides by 22 to get rid of the fraction: 2U=kx22U = kx^2.
  3. Take square root: Next, divide both sides by kk to isolate x2x^2: 2Uk=x2\frac{2U}{k} = x^2.
  4. Take square root: Next, divide both sides by kk to isolate x2x^2: (2U)/k=x2(2U)/k = x^2. Now, take the square root of both sides to solve for xx: x=(2U)/kx = \sqrt{(2U)/k}.

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