# Work/Potential Energy of a Spring

by JJBrian
Tags: energy, spring, work or potential
 P: 20 1. The problem statement, all variables and given/known data a)how much work is done by gravity as a 2kg mass is raised 2m vertically? b)what is the change in gravitation potential energy of a 2kg mass raised 2m vertically? c)How much work is done by a spring with a spring constant k = 50N/m as it is compressed by 0.1m from its relaxed position? d) what is the change in the potential energy of a spring with spring constant k = 50N/m as it is compressed by0.1m from is relaxed position? e) A 0.05kg mass is held against a spring( with spring constant k = 50N/m) while the spring is compressed by 0.1m. The mass is released and accelerated by the spring. What is the final speed of the mass? 3. The attempt at a solution A. Wg= mgh wg = (2)(9.8)(2) = 39.2J B. PE = mgh PE = (2)(9.8)(2) = 39.2J C. Ws = 1/2kx^2 Ws = 1/2(50)(.1)^2 = 0.25J D. Us = 1/2 kx^2 Us = 1/2(50)(.1)^2 = 0.25J E. I dont know.... W = change KE attempt 1/2kx^2 = 1/2mv^2 1/2(50)(.1)^2 = 1/2(.005)v^2 vf = sqrt(10)m/s can someone check my work? I need some help and explanation for problem e. Im not too sure about the signs.
 HW Helper P: 5,004 You seem to be missing a few negative signs...It might help you to find them by looking at the definition of work done by any force $\textbf{F}$ in moving an object form point $\textbf{a}$ to point $\textbf{b}$...what is that definition (it involves an integral and a dot product)?

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