Question

A spring has k = 88 N/m. Use a graph to determine the work needed to stretch it from x = 3.6 cm to x = 5.6 cm, where x is the displacement from its unstretched length.

Answer 1

You don't really need to draw a graph to figure that out. We can't draw them for you here, anyway. You will have to convert the 3.6 cm to 0.036 m and the 5.6 cm to 0.056 m.

The answer is k[(.056)^2 - (.036)^2]
If you used a graph to do it, you should plot the force kx vs x and measure tha area under the curve from x = 0.036 to x = 0.056. You should get the same answer, since the area is a trapezoid with width 0.020 and average height 0.046.

Answer 2

but when you did this.... k[(.056)^2 - (.036)^2]

k = 88 right?

88(.056^2 - .036^2)

then the answer would be .16192? it said that its incorrect. im alittle confused?

Answer 3

It's because, you the equation is

1/2(K)(x^2)

So you change the cm to meters, and then you subtract, getting (.02) then you get (.02)^2, cuz u have to square it,

Then you * by K which is 88, and then divide by 2. That gives you the SPE, (spring potential energy)