How Do You Calculate Spring Constant and Package Weight?

[queenspublic]

1. Problem

A spring with a pointer attached is hanging next to a scale marked in millimeters. Three different packages are hung from the spring, in turn, as shown below.

(a) Which mark on the scale will the pointer indicate when no package is hung from the spring?
(a) ? mm

(b) What is the weight W of the third package?
(b) ? N

2. Attempt at a solution

240 N - 110 N = 130 N
60 mm - 40 mm = 20 mm

130 N = -k * 20 mm <-- Is this formula correct? If not, how do I find the answers to (a) and (b)?
k = -6.5

 

[queenspublic]

Never mind. I found the answers.

(a) 23 mm
(b) 45 N

Thanks for nothing. lol.

 

[nlightner]

N/mm

To find the answers to (a) and (b), we need to use the formula for the spring constant, which is
k = F/x, where k is the spring constant, F is the force applied to the spring, and x is the displacement of the spring.

For part (a), when no package is hung from the spring, the force applied (F) is zero and the displacement (x) is also zero. Therefore, the spring constant (k) is also zero. This means that the pointer will indicate zero millimeters on the scale.

For part (b), we need to use the formula k = F/x to find the spring constant. Since we are given the displacement (x) of 20 mm and the weight of the third package (W) is unknown, we rearrange the formula to solve for W:
W = k * x

Substituting in the value of the spring constant (k = -6.5 N/mm) and the displacement (x = 20 mm), we get:
W = -6.5 N/mm * 20 mm = -130 N

Therefore, the weight of the third package is -130 N or 130 N downwards.