Spring Force Constant?

In summary, the conversation discussed the calculation of the force constant of a spring using the given mass and stretching distance. It was determined that the relationship between force and stretching distance can be approximated using Hooke's law, and the resulting force constant was calculated to be 7.84 N/m. The importance of including units in calculations was also emphasized.]
  • #1
ConstableZiM
10
0

Homework Statement



A 100g object is suspended from a spring. When 40g are added, the spring stretches an additional 5.0cm. With the total mass of 140g, the spring is set into vertical oscillations with an amplitude of 10 cm. (a) What is the force constant of the spring?



Homework Equations


[tex]\sum[/tex] F = 0 = -kx + mg



The Attempt at a Solution



From what I know, the force required to stretch a spring is not linear, so I am guessing that plugging just the 40 grams and the 5 cm into the equation won't work... What I got when I did that was k = 0.040kg * 9.8 / 0.05m = 7.84

Im guessing this is wrong?

Help would be appreciated.
 
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  • #2
The usual assumption about springs is that the force exerted by them is indeed linear (as in #2 above). All your solution needs is units. (Not all information given in the problem is necessary to solve it.)
 
  • #3
ConstableZiM said:
From what I know, the force required to stretch a spring is not linear, so I am guessing that plugging just the 40 grams and the 5 cm into the equation won't work...
Even for a real-world spring, as long as you don't stretch the spring so much that it plastically deforms or collapses onto itself, the relationship between force and stretching distance can be approximated quite well using Hooke's law, F = kx (some authors define it as F = -kx). Here F is directly proportional to x, so it is linear.
What I got when I did that was k = 0.040kg * 9.8 / 0.05m = 7.84
'Looks okay to me. :approve:

[Edit: SEngstrom beat me to the answer. And as SEngstrom says, don't forget your units. :smile:]
 
  • #4
I love you guys ;,[
 
  • #5


I would approach this problem by first defining the variables and equations involved. The spring force constant, also known as the spring constant, is a measure of the stiffness of the spring and is denoted by the letter k. It is defined as the force required to stretch or compress a spring by a unit length, and is expressed in units of N/m (newtons per meter).

In this problem, we are given the mass of the object (100g) and the additional mass added (40g), as well as the change in length of the spring (5.0cm). From this information, we can use the equation F = -kx + mg, where F is the net force on the spring, x is the change in length, and mg is the weight of the object.

To solve for the force constant, we need to rearrange the equation to solve for k. This gives us k = (F + mg)/x. Plugging in the values given, we get k = (0.14kg * 9.8m/s^2)/(0.05m) = 27.44 N/m.

This means that for every 1 meter of length change, the spring exerts a force of 27.44 Newtons.

In the second part of the problem, we are given the amplitude of the oscillations (10cm) and asked to find the force constant again. This time, we can use the equation F = -kx, where F is the force exerted by the spring and x is the displacement from equilibrium.

Since the amplitude is half of the total displacement, we can use the amplitude as the value for x. This gives us a force of F = -k(0.10m) = -2.744 N.

Using the equation F = ma, we can solve for the acceleration of the object, which is equal to the frequency of the oscillations squared multiplied by the amplitude. This gives us a = (2π/T)^2 * 0.10m = 0.157 m/s^2.

Now, we can use the equation F = ma to solve for the spring constant k. This gives us k = F/a = -2.744/0.157 = -17.47 N/m.

The negative sign indicates that the force exerted by the spring is in the opposite direction of the displacement, as expected
 

What is the definition of Spring Force Constant?

The Spring Force Constant, also known as the spring constant, is a measure of the stiffness of a spring. It represents the amount of force required to stretch or compress a spring by a certain length.

How is Spring Force Constant calculated?

The Spring Force Constant can be calculated by dividing the force applied to the spring by the displacement or change in length of the spring. It is represented by the equation F = kx, where F is the force, k is the spring constant, and x is the displacement.

What is the unit of measurement for Spring Force Constant?

The unit of measurement for Spring Force Constant is Newtons per meter (N/m). This unit represents the amount of force required to stretch or compress a spring by one meter.

How does Spring Force Constant affect the behavior of a spring?

A higher Spring Force Constant indicates a stiffer spring, meaning it will require more force to stretch or compress it. On the other hand, a lower Spring Force Constant indicates a more flexible spring, which will require less force to change its length. This affects the spring's behavior in terms of its ability to store and release energy, as well as its resonance frequency and oscillation amplitude.

Can Spring Force Constant vary for different types of springs?

Yes, the Spring Force Constant can vary for different types of springs. It depends on factors such as the material and shape of the spring, as well as the number of coils. For example, a metal spring will have a higher Spring Force Constant compared to a rubber spring of the same size. Additionally, the Spring Force Constant can also vary for the same type of spring depending on its length and thickness.

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