Math Problem Statement
A simple harmonic oscillator moves under the influence of Hooke's law with force F with arrows = −kx with arrow where x with arrow is the displacement from equilibrium. The spring constant k is given by the following equation. k =
F with arrows
x with arrow
= Fs x When an object of mass m = 9 g hangs from the spring, the force stretching the spring is Fs = mg =
⨯ 10−3 kg
9.80 m/s2
= N.
Solution
Let’s solve this step by step.
-
Spring Force Formula: According to Hooke's Law, the force stretching the spring is proportional to the displacement and can be expressed as . The spring constant can then be derived as .
-
Weight of the Mass: The force stretching the spring due to gravity is given by: where is the mass of the object and is the acceleration due to gravity.
-
Substitute Values for : The mass , and .
Calculate :
Final Answer:
The force stretching the spring is:
Let me know if you would like assistance in calculating the spring constant or solving related problems.
Follow-Up Questions:
- How is the displacement related to the spring constant ?
- What would be the spring constant if the displacement is given as ?
- How does increasing the mass affect the stretching force on the spring?
- Can you derive the formula for in terms of mass and displacement?
- What assumptions are made in this problem for simplicity?
Tip: Always keep units consistent while solving physics problems!
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Math Problem Analysis
Mathematical Concepts
Classical Mechanics
Hooke's Law
Force Calculation
Unit Conversion
Formulas
Hooke's Law: F = kx
Spring Constant: k = F/x
Force due to Gravity: F = mg
Theorems
Hooke's Law
Suitable Grade Level
Grades 9-12
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