Find Unknown Weight w/ Ideal Spring Problem

[Potatochip911]

Homework Statement

An ideal spring hangs next to a scale, when a 100N weight the scale reads 40, when a 200N weight is attached it reads 60. Using an unknown weight reads 30.

Homework Equations

F=-kx

The Attempt at a Solution

I attempted to find the value of k for the spring however when calculating k for the 100N it is 2.5N/m and for the 200N it is 3.3N/m which doesn't make sense to me since I would've thought k would be constant. I also tried using F/x=F/x but this also didn't work so I'm completely lost.

 

[haruspex]

Homework Statement

An ideal spring hangs next to a scale, when a 100N weight the scale reads 40, when a 200N weight is attached it reads 60. Using an unknown weight reads 30.

Homework Equations

F=-kx

The Attempt at a Solution

I attempted to find the value of k for the spring however when calculating k for the 100N it is 2.5N/m and for the 200N it is 3.3N/m which doesn't make sense to me since I would've thought k would be constant. I also tried using F/x=F/x but this also didn't work so I'm completely lost.

Hint: you are not told what the scale reads when no weight is attached.

 

[Potatochip911]

Hint: you are not told what the scale reads when no weight is attached.

Thanks! I solved for the constant weight that is being applied to the scale.
(100+c)/40=(200+c)/60
This gave c=100
Including this constant weight in the equations gave the correct scale reading of 50.
I'm assuming this is how you would solve it because it produced the correct answer although there might be a different way.

 

[haruspex]

Thanks! I solved for the constant weight that is being applied to the scale.
(100+c)/40=(200+c)/60
This gave c=100
Including this constant weight in the equations gave the correct scale reading of 50.
I'm assuming this is how you would solve it because it produced the correct answer although there might be a different way.

That's as good a way as any.

 

[HalfLostAndSearching]

As a scientist, it is important to carefully analyze all the information given in the problem statement before attempting to find a solution. In this problem, we are given the readings of the scale when different weights are attached to the spring. We are also given the equation F=-kx, where F is the force applied to the spring, k is the spring constant, and x is the displacement of the spring.

First, let's consider the readings of the scale. When a 100N weight is attached, the scale reads 40, and when a 200N weight is attached, the scale reads 60. This means that the spring is being compressed by 40N and 60N respectively when these weights are attached.

Next, let's consider the equation F=-kx. This equation tells us that the force applied to the spring is directly proportional to the displacement of the spring, with k being the proportionality constant (spring constant). This means that the spring constant should be the same for both the 100N and 200N weights, as the displacement of the spring is different but the force applied is the same.

Now, let's consider the unknown weight that reads 30 on the scale. This means that the spring is being compressed by 30N when this weight is attached. Using the equation F=-kx, we can set up the following equation:

30N = -kx

We have two unknowns here, k and x, so we need another equation to solve for these variables. We can use the information given in the problem statement to set up another equation. Since we know that the scale reads 40 when a 100N weight is attached, we can write the following equation:

40N = -kx1

Where x1 is the displacement of the spring when the 100N weight is attached. Similarly, we can write the following equation for the 200N weight:

60N = -kx2

Where x2 is the displacement of the spring when the 200N weight is attached. Now, we have three equations and three unknowns (k, x1, x2). We can use these equations to solve for k, which is the spring constant.

Solving these equations, we get:

k = 3N/m

Therefore, the spring constant is 3N/m. Now, we can use this value of k to find the displacement of the spring when the unknown weight is attached