Spring Question? How much does the block move?

[lu6cifer]

A spring with a pointer attached is hanging next to a scale marked in millimeters. Three different packages are hung from the spring. W1 is 110 N, and hangs 40mm from the spring, W2 is 240N and hangs 60mm from the spring W3 is x N and hangs 30 mm from the springWhat mark on the scale will the pointer indicate when no package is hung from the spring?

What is the weight W of the 3rd package?

W = -1/2k(x₂²-x₁²)

One thing I wasn't sure about was this equation--are x1 and x2 in the correct order here because you're looking at the work done to stretch a spring?

3. I figured out that I had to create a system of equations from the two given weights, 110 N and 240 N, using the equation above. After converting mm to meters, I got two equations--

14.4 = -0.0018k + 0.5kx₁²
4.4 = -0.0008k + 0.5x₁²

I solved for k, got -10,000, and plugged back in, and got a length of 26.8 m--is that right? Because my online homework thing tells me I'm wrong...

 

[LowlyPion]

I think you have the wrong equation. The problem is about Forces, not Work.

Consider using F = -k*x

 

[thomate1]

I would like to clarify the question and the given information. The question asks for the mark on the scale when no package is hung from the spring, but the information provided includes three packages with their respective weights and distances from the spring. It is not clear if the scale is being used to measure the distance or the weight of the packages.

To answer the question, we need to know the spring constant (k) of the spring, which is not given in the information provided. Without the value of k, we cannot accurately determine the mark on the scale when no package is hung from the spring.

Regarding the equation given, W = -1/2k(x22-x12), it is correct. However, as you pointed out, the order of x1 and x2 needs to be consistent with the direction of the work done. In this case, x1 should be the initial length of the spring and x2 should be the final length after the package is hung.

To determine the weight of the third package (W3), we need to know the value of k and the distance (x3) that the package hangs from the spring. Without this information, we cannot accurately determine the weight of the third package.

In conclusion, to accurately answer the question and determine the weight of the third package, we need to know the value of the spring constant (k) and the distance (x3) that the package hangs from the spring.