Work, Energy question?Please help!?

Question

An ideal spring has a compression force constant of 40 N/m.
a) Use the grid provide to draw a force-compression graph for the spring.
Ok so the x-axis says Compression (m) and has 0, 0.1, 0.2, 0.3 and 0.4.
The y-axis has Force(N).
I used F = kx to get the following coordinates:
(.1,4)
(,2,8)
(.3,12)
(.4,16).
Is that right?
b) Use the graph to determine how much work is done in compressing the spring from
i) 0.0 to 0.1m
ii) 0.1 to 0.2m
OK so if u use W = Fx,
then you get for i) W = 0.1 x 4 = .4 J
But if u work it out like this:
Us = 1/2 kx^2, u get something else:
1/2 x 40 x .1^2
= .2 J?
So which equation is correct? I'm assuming my teacher wants me to use the first equation, because she specifically says 'Use the graph to determine...' but is it right? Why don't the two equations match up???

If u could explain the concept and why I'm getting it wrong, that would be great thanks!!

Answer 1

Your answer to a) is correct. The area under the line between 0.1 and 0 is the work to compress the spring that distance, and likewise for 0.2 to 0.1. You need to use no equations for this problem. Note that in answerman's answer he only addressed 0.1 to 0, which is a triangle, but not 0.2 to 0.1, which is a rectangle and a triangle. It was coincidence he got the same answer as your energy equation - that is not the one to use - read further...

If you did want to use equations, Us is the stored energy in the spring, not the work to compress it. And, W is variable as a spring is being compressed, so you actually need to use an integral to figure it (specifically W=integral from a to b of F(x)dx. Doing an integral is the equivalent to finding the area under a curve.

Hope this helps.

Answer 2

How much work is done in compressing the spring from
i) 0.0 to 0.1m

In the given problem
F = 0 when x = 0
F = 4 when x = 0.1

The 'F' changes from 0 to 4 when x changes from 0 to 0.1.

Initially there was no force [F= 0] and after words F gradually increases from 0 to4 when x changes from 0 to 0.1.

To find the work done for a displacement of 0 to 0.1 that is for a displacement of 0.1 -0 = 01, we must find the average force exerted during this displacement.

Therefore the force that is to be used in the formula is not 4, but the average of 4to 0.

The average force is [4 + 0] / 2 or 1/2 {4-0]

Thus the F to be used in the formula = 2.

Now W = 2 x [0.1] = 0.2 J.

If you use 1/2 k x^2

W = 1/2 [40] [0.1] ^2 = 0.2 J

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How much work is done in compressing the spring from
ii) 0.1 to 0.2m

The displacement is 0.2 ─ 0.1 = 0.1

The average force in this case is [8 + 4] /2 = 6.

W = 6 x 0.1 = 0.6 J.

Using 1/2 kx^2,

First we find the work done from 0 to 0.2

1/2 x40 x 0.2^2 = 0.8 J

Then we subtract the work done from 0to 0.1

1/2 x40 x 0.1^2 = 0.2 J

Work done from 0.1 to 0.2 = 0.8 ─ 0.2 = 0.6 J

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Answer 3

The work done in compressing the spring is the area under the force-vs-distance graph.
From x = 0.0 to x = 0.1 This is a triangle with altitude 4 N
W = (1/2)(0.1)(4) = 0.2 J
From x = 0.1 to x = 0.2 This is a trapezoid with altitudes 4 N and 8N
W = (1/2)(8 + 4)(0.1) = 0.6 J
The equation W = Fx only holds for constant force.

Answer 4

Work is the AREA under the line on the graph. Since it is a triangle A = 1/2bh
therefore
W = 1/2(0.1-0)(4-0) = 0.2J which is exactly what you get with the energy equation...

Answer 5

the difficulty with this simplistic analogy is that this is impossible to tension capability to supply count. It happens at very small scales, yet because of the fact of entropy, unfastened capability or capability interior the style of sunshine or warmth is plenty plenty greater in all likelihood than capability being compelled to be based mass. The opposite technique, besides the undeniable fact that, is completed. Nuclear explosions are a results of the opposite technique, this is, mass changing into capability. this is going to be pointed out that no longer all the uranium/plutonium mass is annihilated in a reaction, so which you do no longer see explosions which might cripple the international ( that little 9x10^sixteen joules you have up there). purely a small volume of the textile certainly annihilates. to comprehend in simple terms how severe it is, in simple terms open a e book and investigate the recommend existence of a particle which includes a pion, which provides up the tremendous majority of its mass while it decays into an electron/positron and photon.