This problem is driving me crazy

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SUMMARY

This discussion revolves around the application of Hooke's Law to determine the equilibrium point of a spring scale when different weights are applied. Weight A, weighing 111 N, displaces the spring to 40 mm, while Weight B, weighing 199 N, displaces it to 60 mm. The user is attempting to find the scale's reading when no weight is applied and the weight of an unknown package C, which displaces the spring to 30 mm. The user correctly identifies the relationship between force and displacement, applying the formula F = kx to analyze the spring's behavior.

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  • Understanding of Hooke's Law (F = kx)
  • Basic knowledge of force and weight measurements in Newtons
  • Familiarity with spring scale mechanics
  • Ability to interpret displacement measurements in millimeters
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  • Research the calculation of spring constants using Hooke's Law
  • Learn how to determine the equilibrium position of a spring system
  • Explore the relationship between force, mass, and acceleration in physics
  • Investigate practical applications of spring scales in various scientific experiments
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Students studying physics, particularly those focusing on mechanics and spring dynamics, as well as educators looking for practical examples of Hooke's Law in action.

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Homework Statement


A spring with a pointer attached is hanging next to a scale marked in millimeters. Three different weights (weights A, B and C) are hung from the spring, in turn, as shown below. Weight A weighs 111 N and B weighs 199 N.

there are three pictures of spring scales with weights attached: the first spring with weight A attached is at 40mm the second (with weight B) is at 60mm and the third (with weight C) is at 30mm

(1) Which mark on the scale will the pointer indicate when no package is hung from the spring?
(2) What is the weight of package C?

The Attempt at a Solution


right now I'm just thinking about part 1 so i found the difference in mm and N between A and B so i found 20mm and 88N and I'm pretty sure this is relevant, but I'm really confused and don't know where to go from here!
 
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The first part is basically just asking you to figure out the equilibrium point of the spring. When the mass is hanging from the spring, what keeps the mass from just falling to the floor? Just what does hooke's law say?
 
so F=kx
88=k20
so the answer would be 4.4?
 
Hooke's law says that the force is proportional to the spring constant and the displacement.

F = -k \Delta x
 
ok i think I'm starting to get it now...thanks
 

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