Hooke's Law and Springs

In summary, Hooke's law describes a light spring with an unstressed length of 35.0 cm. When a 5.40 kg object is hung from one end and attached to a door frame, the spring's length becomes 42.00 cm. Using the equation F=Kx, the spring constant is found to be 756 N/m. When the load and spring are taken down and two people pull in opposite directions with a force of 150 N each, the length of the spring becomes 0.74 m. However, if only one person is pulling with a force of 150 N, the length becomes 0.54 m. This can be explained by the fact that force is a vector and the
  • #1
Gandor481
2
1

Homework Statement



Hooke's law describes a certain light spring of unstressed length 35.0 cm. When one end is attached to the top of a door frame and a 5.40 kg object is hung from the other end, the length of the spring is 42.00 cm.
(a) Find its spring constant.



(b) The load and the spring are taken down. Two people pull in opposite directions on the ends of the spring, each with a force of 150 N. Find the length of the spring in this situation.



Homework Equations



F=Kx

The Attempt at a Solution



A)
The spring constant is equal to
mg=kx
5.40*9.8=k*(.42-.35)
52.92=k(.07)
k=756 Nm

B)
∑F=150+150=300
300=kx
300/k=x
x=.39m

.39+.35=.74m

Which according to the book the correct answer is .54m which I was able to get if I only accounted for 150N being pulled instead of 300N since 150N is being pulled from both sides of the spring. I don't understand why it would only be 150N?
 
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  • #2
Consider - when it was haging from the door, the weight pulled it by mg and the door pulled in the opposite direcetion by mg, yet you didn't say that kx=2mg did you? Why not?

Replace one of the people by a pole stuck in the ground - you get 150N one way due to the other person, and 150N the other way from the pole.

Note: force is a vector - so the total force on the spring is actually zero.
 

1. What is Hooke's Law?

Hooke's Law is a principle in physics that states that the force needed to extend or compress a spring by some distance is directly proportional to that distance. This law was discovered by Robert Hooke in the 17th century.

2. How is Hooke's Law expressed mathematically?

Hooke's Law is expressed as F = -kx, where F is the force applied to the spring, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

3. What is the significance of the spring constant in Hooke's Law?

The spring constant, denoted by k, is a measure of the stiffness of a spring. It is a constant specific to each spring and is determined by factors such as the material and shape of the spring. It determines the amount of force needed to extend or compress the spring by a certain distance.

4. Can Hooke's Law be applied to all types of springs?

Hooke's Law can be applied to most springs as long as the spring is within its elastic limit. The elastic limit is the point at which a spring will no longer return to its original shape when the force is removed, and the relationship between force and displacement is no longer linear.

5. How is Hooke's Law used in practical applications?

Hooke's Law is used in various practical applications, such as in the design of suspension systems for vehicles, measuring devices like spring scales, and as a basis for calculating the elastic modulus of materials. It is also used in engineering and construction to determine the appropriate tension in cables and wires.

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