A graph of the potential energy stored in a tendon as a function of the square o

Question

A graph of the potential energy stored in a tendon as a function of the square of the distance x it has stretched from its equilibrium position is shown in the accompanying figure

http://session.masteringphysics.com/problemAsset/1343058/2/1027473.jpg

A.How far must the tendon be stretched from its equilibrium position to store 10.0J of energy?

B.What is the force constant of the tendon?

C. What force is necessary to hold the tendon in place in part A?

D.Sketch a clear graph of the potential energy stored in the tendon as a function of x.

Explanation / Answer

since its linear wrt x^2

U=px^2, at x^2 =0.02, U = 2, p = 2/0.02 = 100

U = 100*x^2,

1. 10 J = 100*x^2 => x^2 = 0.1 => x = 10 = 3.1622 m

2. tendon is like a spring, for a spring with force constant k, U = 0.5*k*x^2

here, p=100, force constant = 100/0.5 = 200N/m

3. x = 3.166m found in part 1.

force = -k*x = -200*3.1622 = -632.455 N

4. graph will be U vs x, U = 100*x^2, quadratic in nature passing through origin

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