As illustrated in the figure, a spring with spring constant k is stretched from

Question

As illustrated in the figure, a spring with spring constant k is stretched from x=0 to x=3d, where x=0 is the equilibrium position of the spring.

Part C

Now consider two springs A and B that are attached to a wall. Spring A has a spring constant that is four times that of the spring constant of spring B. If the same amount of energy is required to stretch both springs, what can be said about the distance each spring is stretched?

By the way, does any one know the answer of part D? Thank you

Explanation / Answer

We can solve algebraically using the equation for spring potential energy: U = 1/2kx^2

Spring A:

U = 1/2kx^2

Spring B:

Since k is 1/4 that of spring A:

U = 1/2(1/4k)x^2
U = 1/8kx^2

Set the equations for spring A and B equal to each other and solve for the x’es

1/2kxA^2 = 1/8kxB^2
kxA^2 = 1/4kxB^2
xA^2 = 1/4xB^2

Squareroot:

xA = 1/2xB

So:

Spring A must stretch half the distance spring B stretches.

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