How to Determine the Block's Position After Applying Force to a Spring?

[queenspublic]

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 * (x_f² - x_i²)
(+63 N)î = -k(-2.0 cm)î k = 3.15 x 10³ N/M
x_i= -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.

 

[Doc Al]

I got some weird decimal answer which was apparently wrong.

What did you get?

I also don't understand what the smaller and larger value is.

You could move the block in either direction.

 

[queenspublic]

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]

How did you get the answer of 0.4? (40 cm?) The equation you posted previously looked OK to me. Did you solve it?

 

[queenspublic]

Yeah, I got x_f = 0.4 cm.

 

[Doc Al]

Yeah, I got x_f = 0.4 cm.

Redo your solution. (And check your answer by plugging back into the original equation and seeing if it works.)

 

[queenspublic]

I got 2 this time. Am I suppose to convert that to something?

 

[Doc Al]

+4.1 J = (1/2)k * (x_f² - x_i²)

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.

 

[queenspublic]

I got 2. I'm sure.

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

 

[Doc Al]

I got 2. I'm sure.

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

Use standard units: 2.0 cm → 0.02 m.

 

[queenspublic]

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]

That looks better.

 

[queenspublic]

Okay, I get 160.7. Do I have to convert that or something?

 

[Doc Al]

Please double-check that answer. (Is 160 m a reasonable answer?)

 

[queenspublic]

It's wrong. I got 160.

 

[Doc Al]

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) = ?

 

[queenspublic]

A = 25830
B = 4e-4
A + B = 25830.0004
? = 160.7

I tried 161, it's also wrong.

 

[Doc Al]

A = 25830

Way off. (You're probably multiplying where you should be dividing.)

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

 

[queenspublic]

o wait a second...you're right

 

[queenspublic]

I got .0027. Do I have to convert this?

 

[Doc Al]

I got .0027. Do I have to convert this?

No conversions needed.

 

[queenspublic]

My final answer is .0557, do I have to convert this answer?

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

 

[Doc Al]

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.