Hooke's law (confirmation if I did it right)

In summary, Hooke's Law is a physical law discovered by English scientist Robert Hooke in the 17th century. It states that the force required to extend or compress a spring is directly proportional to the distance the spring is extended or compressed from its original position. The mathematical equation, F = -kx, represents the force applied, the spring's stiffness, and the distance it is extended or compressed. However, Hooke's Law is only applicable to elastic materials that can return to their original shape. It is used in various real-life applications, such as designing and calibrating springs for cars, doors, and mattresses, as well as in fields like engineering, physics, and biomechanics to analyze material behavior under stress.
  • #1
mathnoobie
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Homework Statement


Seven and one half foot pounds of work is required to compress a spring 2 inches from its natural length. Find the work required to compress the spring an additional one-half inch


Homework Equations


W=kd
W=∫f(x)dx


The Attempt at a Solution


7.5=W
∫kxdx from (0,1/6)
=(kx^(2))/2 from (0,1/6)
=k/72=7.5
K=540

∫(540x)dx from (4/24, 5/24)

The rest is just algebra that's irrelevant; did i set up the problem right?
 
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  • #2
Yes, that is correct.
 

FAQ: Hooke's law (confirmation if I did it right)

What is Hooke's Law?

Hooke's Law is a physical law that states the force required to extend or compress a spring is directly proportional to the distance the spring is extended or compressed from its original position.

Who discovered Hooke's Law?

Hooke's Law was discovered by English scientist Robert Hooke in the 17th century.

What does the mathematical equation for Hooke's Law represent?

The equation, F = -kx, represents the force (F) applied to an object, the spring's stiffness or spring constant (k), and the distance the spring is extended or compressed (x).

Is Hooke's Law applicable to all materials?

No, Hooke's Law is only applicable to elastic materials, such as springs, that can return to their original shape after being stretched or compressed.

How is Hooke's Law used in real-life applications?

Hooke's Law is used in a variety of real-life applications, including designing and calibrating springs for various purposes, such as car suspensions, door hinges, and mattresses. It is also used in fields such as engineering, physics, and biomechanics to understand and analyze the behavior of materials under stress.

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