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Work Done by a Spring Force (NEED HELP QUICK!)

1. Problem

In the figure, we must apply a force of magnitude 63 N to hold the block stationary at x = -2.0 cm. From that position we then slowly move the block so that our force does +4.1 J of work on the spring-block system; the block is then again stationary. What is the block's position (x)? (There are two answers.)

Here's the figure: http://www.webassign.net/hrw/7-11a.gif

? cm (smaller value)
? cm (larger value)

2. Attempt at a solution

+4.1 J = (1/2)k * (xf2 - xi2)
(+63 N)î = -k(-2.0 cm)î k = 3.15 x 103 N/M
xi= -2.0 cm

I got some weird decimal answer which was apparently wrong.
I also don't understand what the smaller and larger value is.
 
Last edited by a moderator:

Doc Al

Mentor
44,766
1,044
0.4

So the smaller value is negative and the larger value is positive, am I right?. I tried -0.4 too. It's wrong.
 

Doc Al

Mentor
44,766
1,044
How did you get the answer of 0.4? (40 cm?) The equation you posted previously looked OK to me. Did you solve it?
 
Yeah, I got xf = 0.4 cm.
 

Doc Al

Mentor
44,766
1,044
I got 2 this time. Am I suppose to convert that to something?
 

Doc Al

Mentor
44,766
1,044
+4.1 J = (1/2)k * (xf2 - xi2)
This is the equation you're solving, right? When you get an answer, plug it back into the equation to verify it.

How are you solving it? Show each step along the way.
 
I got 2. I'm sure.

Square root of this [4.1 / (1/2)(3.15 x 103) + (-2.0)2]
 

Doc Al

Mentor
44,766
1,044
Ah crap, you're right.

So it's...Square root of this [4.1 / (1/2)(3.15 x 103) + (-2.0 x 10-2)2]
 

Doc Al

Mentor
44,766
1,044
That looks better.
 
Okay, I get 160.7. Do I have to convert that or something?
 

Doc Al

Mentor
44,766
1,044
Please double-check that answer. (Is 160 m a reasonable answer?)
 
It's wrong. I got 160.
 

Doc Al

Mentor
44,766
1,044
So it's...Square root of this [4.1 / (1/2)(3.15 x 103) + (-2.0 x 10-2)2]
Let's do it step by step.

A = 4.1 / (1/2)(3.15 x 103) = ?

B = (-2.0 x 10-2)2 = ?

A + B = ?

√(A + B) = ?
 
A = 25830
B = 4e-4
A + B = 25830.0004
? = 160.7

I tried 161, it's also wrong.
 

Doc Al

Mentor
44,766
1,044
o wait a second...you're right
 
I got .0027. Do I have to convert this?
 
My final answer is .0557, do I have to convert this answer?

I'm getting multiple answers. Second time, I got .0548.
 
Last edited:

Doc Al

Mentor
44,766
1,044
My final answer is .0557, do I have to convert this answer?

I'm getting multiple answers. Second time, I got .0548.
The second one is correct--at least it's the same answer I get. (You're getting multiple answers, most likely, because you are rounding off different parts of your solution.)

Since it's a distance, the answer is in meters. If you want the answer in cm, then you can convert.
 

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