Solve Spring Force Homework: Mass, Lower Spring & Compression Length

[tibessiba]

Homework Statement

A 6.90 mass hanging from a spring scale is slowly lowered onto a vertical spring, as shown in the figure.

What does the spring scale read just before the mass touches the lower spring? --> I calculated this to be F= 67.6 N just using m*g.

The second question is:
The scale reads 24.0 N when the lower spring has been compressed by 2.70cm . What is the value of the spring constant for the lower spring?

k = ? N/m

The third question is:
At what compression length will the scale read zero?
delta y = ? cm

Homework Equations

For the second question I tried using the equation k = F_spring/delta s

The Attempt at a Solution

My attempted to use this formula to get k = 24 N/0.027 m which was equal to 888.9 N/m. However this is not correct. Can anyone tell me where I went wrong?

 

[learningphysics]

You're using F_spring of the upper spring, to find the spring constant of the lower spring...

If the upper spring is reading 24N... that means the upper spring is exerting an upward force of 24N on the mass...

The lower spring exerts an upward force of kx = k(0.027)

And then there's the weight of the mass acting downwards...

What is the vector sum of these 3 forces? use that to solve for k.

 

[tibessiba]

Ok, Thank You! I got it. I took 24N - 67.7N and then divided that by 0.027m to get -1614.8N/m.

But now the next question is:

At what compression length will the scale read zero?

delta y = ? cm

Do I just take the total force (67.7N) and divide it by the spring constant?? (and convert to cm)?