# Finding Work Done by a Spring Force on a Pen

• maw07005
In summary, the problem involves a pen with a spring of 221 N/m spring constant. The pen is initially compressed 4.90 mm and then an additional 5.20 mm in order to be ready for writing. The question asks for the work done by the spring force, with the proper algebraic sign. The equation for elastic potential energy is given, but this is not the same as work. The work done by a force can be positive, negative, or zero. They want to know the algebraic sign and value of the work done by the spring.
maw07005

## Homework Statement

A pen contains a spring with a spring constant of 221 N/m. Whe the tip of the pen is in its retracted position, the spring is compressed 4.90 mm from its unstrained length. In order to push the tip out and lock it into its writing position, the spring must be compressed an additional 5.20 mm. How much work is done by the spring force to ready the pen for writing? Be sure to include the proper algebraic sign with your answer.

W elastic=.5kx^2

## The Attempt at a Solution

I have no idea what they mean by keep an algebraic answer and where does x final come into the equation along with the additional x value.

maw07005 said:

## Homework Statement

A pen contains a spring with a spring constant of 221 N/m. Whe the tip of the pen is in its retracted position, the spring is compressed 4.90 mm from its unstrained length. In order to push the tip out and lock it into its writing position, the spring must be compressed an additional 5.20 mm. How much work is done by the spring force to ready the pen for writing? Be sure to include the proper algebraic sign with your answer.

## Homework Equations

W elastic=.5kx^2
this is the Potential Energy of the spring when it is displaced a distance x from its unstretched position. Don't confuse work with Potential Energy.

## The Attempt at a Solution

I have no idea what they mean by keep an algebraic answer and where does x final come into the equation along with the additional x value.
The work done by a force moving through a distance can be plus or minus (or 0). They want to know here if the work done by the spring is positive or negative (or 0), and what is its value. That's what they mean by an algebraic answer. What do you know about the relationship between the work done by a spring and its potential energy change?

I can provide a response to this content by explaining the concept of work done by a spring force and how to calculate it using the given information.

First, let's define work. Work is the measure of energy transfer that occurs when a force acts on an object and causes it to move a certain distance in the direction of the force. In this case, the force is the spring force acting on the pen and causing it to move when compressed.

The equation for work done by a spring force is W = 0.5kx^2, where k is the spring constant and x is the distance the spring is compressed or stretched.

In this problem, we are given the spring constant (k = 221 N/m) and the initial compression of the spring (x = 4.90 mm). To find the work done by the spring force to ready the pen for writing, we need to calculate the additional compression (Δx = 5.20 mm) and add it to the initial compression (x = 4.90 mm).

So, the total compression of the spring is x = 4.90 mm + 5.20 mm = 10.10 mm = 0.01010 m.

Now, we can plug in the values into the equation for work done by a spring force: W = 0.5(221 N/m)(0.01010 m)^2 = 0.111 Nm = 0.111 J

The algebraic sign for this answer is positive because the spring force is doing work on the pen by pushing it out and locking it into its writing position.

In conclusion, the work done by the spring force to ready the pen for writing is 0.111 J.

## 1. How is work defined in terms of a spring force on a pen?

Work is defined as the product of the force applied to an object and the distance it moves in the direction of that force. In the case of a spring force on a pen, it is the force applied by the spring on the pen multiplied by the distance the pen moves in the direction of the spring force.

## 2. What is the formula for calculating work done by a spring force on a pen?

The formula for calculating work done by a spring force on a pen is W = 1/2 * k * x^2, where W is work done, k is the spring constant, and x is the distance the pen moves in the direction of the spring force.

## 3. How does the spring constant affect the work done by a spring force on a pen?

The spring constant represents the stiffness of the spring and determines how much force the spring exerts for a given displacement. A higher spring constant means the spring is stiffer and will exert a greater force on the pen, resulting in more work being done.

## 4. Can the work done by a spring force on a pen be negative?

Yes, the work done by a spring force on a pen can be negative if the pen moves in the opposite direction of the spring force. This means that the pen is resisting the force of the spring and work is being done against the force.

## 5. How does the displacement of the pen affect the work done by a spring force?

The work done by a spring force on a pen is directly proportional to the displacement of the pen in the direction of the spring force. This means that the further the pen is displaced, the more work will be done by the spring force.

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