# Calculating Work Done by Spring Constant k

• bewger
In summary, the conversation discusses the concept of work done by a spring on a block when it is displaced from one point to another. The force required to hold the block at different points is also mentioned. The equations for calculating the work done by a spring are also provided. Finally, the conversation ends with a question about finding the value of k based on given information.
bewger

## Homework Statement

When the block is pulled out to x = +5.0 cm, we must apply a force of magnitude 460 N to hold it there. We pull the block to x = +12.0 cm and then release it.

The 3 figures can be described by this.

(a) A spring in its relaxed state. The origin of an x-axis has been placed at the end of the spring that is attached to a block.

(b) The block is displaced by dvec, and the spring is stretched by a positive amount x. Note the restoring force Fvecs exerted by the spring.

(c) The spring is compressed by a negative amount x. Again, note the restoring force.

For each of the following, find how much work the spring does on the block when the block moves from the first point given to the second point given
(a) xi = 6.0 cm to x = 4.5 cm
(b) xi = 6.0 cm to x = -4.5 cm
(c) xi = 6.0 cm to x = -6.0 cm
(d) xi = 6.0 cm to x = -12.0 cm

## Homework Equations

F_s = -kd
F_x = -kx

W_s = .5*k*x_i^2 - 0.5*k*x_f^2

## The Attempt at a Solution

How do i get k from what's given?

Is it something like F_x/x = k?

So 460/.05 = 920?

Yep.

## 1. What is the formula for calculating work done by spring constant k?

The formula for calculating work done by spring constant k is W = 1/2 * k * x^2, where W represents the work done, k is the spring constant, and x is the distance the spring is stretched or compressed.

## 2. How do you find the spring constant k?

The spring constant k can be found by dividing the force applied to the spring by the distance the spring is stretched or compressed. This can be represented as k = F/x, where F is the force applied and x is the distance.

## 3. Can the work done by spring constant k be negative?

Yes, the work done by spring constant k can be negative. This means that the spring is releasing stored energy, rather than storing it. This can happen when the spring is compressed or stretched in the opposite direction of the applied force.

## 4. How does the work done by spring constant k relate to potential energy?

The work done by spring constant k is directly related to potential energy. The work done is equal to the change in potential energy, as represented by the formula W = ΔPE. This means that when the spring is stretched or compressed, potential energy is either stored or released.

## 5. Can the work done by spring constant k be used to find the force applied to the spring?

Yes, the work done by spring constant k can be rearranged to find the force applied to the spring. The formula can be rewritten as F = 2 * W/x, where F is the force and W is the work done. This can be useful in determining the force needed to stretch or compress a spring to a certain distance.

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