Help using Hooke's law to find work

In summary, the problem involves using Hooke's Law to determine the variable force in a spring problem. It is given that 18 foot-pounds of work is required to stretch the spring 4 inches from its natural length. The task is to find the work required to stretch the spring an additional 3 inches. Using the equation W=∫f(x)dx, the solution involves setting the work equal to 18 and the distance equal to 4, and solving for the constant k. The resulting function is (18/4)x, which is then integrated from 4 to 7 to get the work required for the additional 3 inches. However, this approach may not be correct and a different approach may be needed.
  • #1
mathnoobie
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Homework Statement


Use Hooke's Law to determine the variable force in spring problem.

Eighteen foot-pounds of work is required to stretch a spring 4 inches from it's natural length. Find the work required to stretch the spring an additional 3 inches.


Homework Equations


W=∫f(x)dx
f=kd


The Attempt at a Solution



I set the work equal to 18 and the distance equal to 4.
so 18=4K, K=18/4
with this knowledge I set my function is (18/4)X
integrating
∫(18x/4)dx from 4 to 7
I get 9x(^2)/4
using the fundamental theorum of Calculus from 4 to 7
I get 74 1/4 (not sure of units, is it inches-pound)
 
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  • #2
You need to start off recognizing that

W - W(t) = ∫0df(x) dx = ∫0d kx dx

If you will re-work the problem with this beginning, I think you will get a totally different outcome.
 

FAQ: Help using Hooke's law to find work

1. How do I use Hooke's law to find work?

To use Hooke's law to find work, you will need to know the spring constant (k) of the object, which is a measure of its stiffness, and the displacement (x) of the object from its equilibrium position. The equation for work (W) using Hooke's law is W = 0.5 * k * x^2. Plug in the values for k and x and solve for W to find the amount of work done on the object.

2. What is Hooke's law and why is it important?

Hooke's law is a principle in physics that states that the force applied to an elastic object is directly proportional to the amount of stretch or compression of the object. It is important because it helps us understand and predict the behavior of elastic objects, such as springs, and can be applied in various fields such as engineering, biomechanics, and materials science.

3. Can Hooke's law be applied to all objects?

No, Hooke's law can only be applied to elastic objects, which are those that can be stretched or compressed and return to their original shape once the force is removed. Non-elastic objects, such as plastic, do not follow Hooke's law and have different properties.

4. How is Hooke's law related to potential energy?

Hooke's law is related to potential energy because the work done on an object by a spring is stored as potential energy. As the object is stretched or compressed, the potential energy increases. The equation for potential energy (PE) using Hooke's law is PE = 0.5 * k * x^2. This potential energy can then be converted into other forms of energy, such as kinetic energy, as the object is released.

5. What are some real-life applications of Hooke's law?

Hooke's law has many real-life applications, such as in designing and analyzing spring-based systems, such as suspension systems in vehicles and shock absorbers. It is also used in biomedical engineering to understand the behavior of tissues and cells, and in materials science to study the elasticity of materials. Hooke's law is also used in everyday objects, such as mattresses, trampolines, and diving boards.

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