Consider the work done by gravity and a spring: (a) Find an expression for the w

Question

Consider the work done by gravity and a spring:

(a) Find an expression for the work done by gravity on a massm as it is raised a distance h vertically.

(b) A spring with constant k is horizontal (ignore gravity)and starts out compressed a distance x. Find work done bythe spring on a mass m when the spring is released andmoves back to its equilibrium position (x=0)

(c) Find the work done by the spring on the mass m if themass starts out at the springs equilibrium (x=0) and compresses thespring a distance of x

(d) Find the work done by the spring on the mass m if themass starts out at the spring equilibrium (x=0) and compresses thespring a distance x

THANKS!!!!!

Explanation / Answer

a)W=F.S (force * displacement)     =W*h (W:weight)     =mgh b)W=integral of F ds (F again is the force)    but F=-kx (for a spring)     integral of kx dx       =k integral of x dx      = 1/2kx2 c) identical as last part...W=1/2kx2

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