Question involving spring constant

[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
But something feels fishy about this, a spring doesn't move down just .053 m

 

[AEM]

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
But something feels fishy about this, a spring doesn't move down just .053 m

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?

 

[kerimek]

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.