Finding the Block's Position After Work is Done on a Spring System

In summary, the problem involves applying a force of 80N to hold a block stationary at x = -2.0cm, then slowly moving the block to do +4.0J of work on the spring-block system. The spring constant is found to be 4000 N/m and using the correct equation, the final position of the block is determined to be a real number. The work done by the person and the work done by the spring have opposite signs due to their directions.
  • #1
Supernejihh
13
0

Homework Statement



We must apply a force of magnitude 80N to hold the block stationary at x = -2.0cm. From that position, we then slowly move the block so that our force does +4.0J of work on the spring-block system; the block is then again stationary. What is the block's position? (Two answers.)


Homework Equations



F = -kx

W = (1/2)*k*xi^2 - (1/2)*k*xf^2


The Attempt at a Solution



80 = -k(-.02m)
k = 4000 N/m

With the spring constant, i plug it into the Work equation to find xf

4 = .5*4000*(-.02^2) - .5*4000*xf^2

3.2 = -2000xf^2
-.0016 = xf^2

And this is where I am stuck. The answer cannot be an imaginary number, but a real one. I know the equations are correct, so what am I doing wrong? Please explain.
 
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  • #2
Supernejihh said:
W = (1/2)*k*xi^2 - (1/2)*k*xf^2
You want final minus initial, not the other way around.
 
  • #3
Doc Al said:
You want final minus initial, not the other way around.

The problem is that, that is how the book presented us with the equation. It was initial minus final. I understand where you are coming from, but that's how it is.
 
  • #4
Supernejihh said:
The problem is that, that is how the book presented us with the equation. It was initial minus final. I understand where you are coming from, but that's how it is.
Then what does W stand for in your book? The work done by the spring? The work done by you will be opposite to that.
 
  • #5
Doc Al said:
Then what does W stand for in your book? The work done by the spring? The work done by you will be opposite to that.

Doc Al. So what you are telling me is that the Work of +4.0J is caused by me. And its positive because the direction and force are directed towards one way. But the force of a spring is always opposite the displacement. So the work of the spring is -4.0J because its moving one way, while the force is directed towards the opposite?
 
  • #6
Supernejihh said:
Doc Al. So what you are telling me is that the Work of +4.0J is caused by me. And its positive because the direction and force are directed towards one way. But the force of a spring is always opposite the displacement. So the work of the spring is -4.0J because its moving one way, while the force is directed towards the opposite?
Right.
 
  • #7
Doc Al said:
Right.

Thanks for your help Doc. I really appreciate it.
 

1. What is work done by a spring?

The work done by a spring refers to the amount of energy that is transferred or converted when a spring is stretched or compressed. This work is typically measured in joules (J) and is a result of the force applied to the spring and the displacement of the spring from its equilibrium position.

2. How is work done by a spring calculated?

The work done by a spring can be calculated using the formula W = 1/2 kx^2, where W is the work done, k is the spring constant, and x is the displacement of the spring from its equilibrium position. The spring constant is a measure of the stiffness of the spring and is typically measured in Newtons per meter (N/m).

3. What factors affect the work done by a spring?

The work done by a spring is affected by the force applied to the spring and the displacement of the spring from its equilibrium position. The spring constant and the mass of the object attached to the spring can also affect the work done. Additionally, the work done may vary depending on whether the spring is being stretched or compressed.

4. What is the relationship between work done and potential energy for a spring?

The work done by a spring is equal to the change in potential energy of the spring. This means that as the spring is stretched or compressed, potential energy is stored in the spring and work is done to transfer or convert this energy. The potential energy of a spring is given by the formula PE = 1/2 kx^2, where k is the spring constant and x is the displacement from equilibrium.

5. How is the work done by a spring related to the Hooke's Law?

The work done by a spring is directly related to Hooke's Law, which states that the force applied to a spring is directly proportional to the displacement of the spring from its equilibrium position. This means that as the displacement increases, so does the force applied to the spring, resulting in a larger work being done. Hooke's Law can also be expressed as F = -kx, where F is the force applied, k is the spring constant, and x is the displacement from equilibrium.

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