# Question involving spring constant

• Phenom66
In summary, the conversation is about finding the new length of a spring with a spring constant of 12000N/m when a 65 kg weight is placed on it. The attempted solution involved using the formula f = kx and converting the weight into Newtons. The final answer may seem unreasonable at first, but after converting to centimeters, it is a reasonable amount for a spring to move.
Phenom66

## Homework Statement

We have a spring that is 30cm with a spring constant of 12000N/m
and there is a 65 kg weight put onto this spring. What is the new length of the spring?

## Homework Equations

f = k *changeof* x

## The Attempt at a Solution

I tried to take 65kg times 9.81 to find Newtons (which is 637.65N)
so therefore 637.65 = 12000 *change of* x
and x = 637.65/12000

Phenom66 said:

## Homework Statement

We have a spring that is 30cm with a spring constant of 12000N/m
and there is a 65 kg weight put onto this spring. What is the new length of the spring?

## Homework Equations

f = k *changeof* x

## The Attempt at a Solution

I tried to take 65kg times 9.81 to find Newtons (which is 637.65N)
so therefore 637.65 = 12000 *change of* x
and x = 637.65/12000

Think about it for a moment longer. How big is 637.65 N compared to 12000 N?

Then convert .053 m into centimeters. Now does it seem so unreasonable?

when you add 65kg to it.

I would first like to commend the effort put into solving this problem. However, I can understand your concern about the result seeming "fishy." The issue with your approach is that it does not take into account the initial length of the spring. The formula you are using, f = k *changeof* x, assumes that the spring is initially at its relaxed length (i.e. no external force acting on it). In this case, the spring is already stretched to 30cm, so the calculation needs to take that into account.

To solve this problem, we can use the equation for the force exerted by a spring, F = kx, where F is the force, k is the spring constant, and x is the displacement from the relaxed length. We know that the force exerted by the weight is 637.65N, so we can set up the following equation:

637.65N = 12000N/m * x

Solving for x, we get x = 0.053 m, which is the same as your result. However, this time it is the displacement from the relaxed length, not the total length of the spring. To find the new length of the spring, we need to add this displacement to the initial length of 30cm, giving us a final length of 30.053cm.

In summary, the approach you used was correct, but it did not take into account the initial length of the spring. By using the equation for the force exerted by a spring, we can accurately calculate the new length of the spring.

## 1. What is spring constant and how is it calculated?

Spring constant, also known as force constant, is a measure of the stiffness of a spring. It is represented by the letter k and is calculated by dividing the force applied to the spring by the displacement it causes.

## 2. How does spring constant affect the behavior of a spring?

The higher the spring constant, the stiffer the spring will be. This means that the spring will resist changes in its length more strongly and will require more force to compress or stretch it. On the other hand, a lower spring constant indicates a more flexible spring that can be easily compressed or stretched.

## 3. What is the unit of measurement for spring constant?

Spring constant is typically measured in units of newtons per meter (N/m) in the metric system or pounds per inch (lb/in) in the imperial system.

## 4. Can spring constant change?

Yes, the spring constant can change if the physical properties of the spring, such as its material or dimensions, are altered. It can also change if the spring is exposed to extreme temperatures or if it is worn out due to repeated use.

## 5. How is spring constant related to Hooke's Law?

Hooke's Law states that the force applied to a spring is directly proportional to the amount of stretch or compression it experiences. The spring constant is the proportionality constant in this relationship, as expressed by the equation F = -kx, where F is the force applied, x is the displacement, and k is the spring constant.

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