Solving Mechanics Statics Homework Problem

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Discussion Overview

The discussion revolves around a mechanics statics homework problem involving forces acting on a rod and a spring. Participants are attempting to analyze the equilibrium conditions and relationships between the forces, angles, and distances involved in the system.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents equations for the forces in the vertical and horizontal directions, noting the presence of three unknowns (d, θ, F(rod)) but only two equations, leading to uncertainty about how to proceed.
  • Another participant suggests a relationship between the distance d and the angle θ, indicating that the force exerted by the spring is dependent on d.
  • A subsequent post provides expressions for cosθ and sinθ in terms of d, leading to a more complex equation that the participant finds challenging to solve due to the presence of a square root.
  • Another participant encourages the use of trigonometric identities to simplify the problem and questions the highest level of math the original poster has completed.
  • A later reply suggests squaring both sides of the equation to eliminate the square root, proposing that the resulting equation may be quadratic.

Areas of Agreement / Disagreement

Participants express uncertainty about how to solve the equations and whether the problem can be simplified. There is no consensus on the best approach to take, and multiple viewpoints on how to handle the mathematical complexity remain present.

Contextual Notes

Participants note the difficulty in solving for d due to the polynomial nature of the resulting equations, and there is mention of the need for familiarity with higher degree polynomials, which may not be fully established among all participants.

Who May Find This Useful

This discussion may be useful for students working on mechanics statics problems, particularly those involving equilibrium and force analysis, as well as those seeking to understand the application of trigonometric relationships in physics.

JeeebeZ
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Homework Statement



http://s11.postimage.org/yvt7eeg35/image.png

Homework Equations



The Attempt at a Solution



So I get that

ƩFy = 0 = F(rod)y - F(weight)

ƩFx = 0 = F(rod)x - F(spring)

F(spring) = 200N * (1.5m + d)
d being the unknown distance that the rod has moved by.

So I get
F(rod) = 60N / sinθ

F(rod) = (200N * (1.5m + d)) / cosθ

Which leaves me with 3 unknowns.
d & θ & F(rod)

But only 2 equations

So I have no idea where to go from here
 
Last edited by a moderator:
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JeeebeZ said:

Homework Statement



http://s11.postimage.org/yvt7eeg35/image.png

Homework Equations



The Attempt at a Solution



So I get that

ƩFy = 0 = F(rod)y - F(weight)

ƩFx = 0 = F(rod)x - F(spring)

F(spring) = 200N * (1.5m + d)
d being the unknown distance that the rod has moved by.

So I get
F(rod) = 60N / sinθ

F(rod) = (200N * (1.5m + d)) / cosθ

Which leaves me with 3 unknowns.
d & θ & F(rod)

But only 2 equations

So I have no idea where to go from here
The equilibrium length of the spring is 1.5 m, so the force exerted by the spring is 200*d.

There is another relationship available. How is d related to θ ?
 
Last edited by a moderator:
So,

cosθ = (1.5 - d) / 1.5

sinθ = √(1.52 - (1.5 - d)2) / 1.5

which would leave me with

60 / √(1.52 - (1.5 - d)2) = 200d / (1.5 - d)

What seems like a really hard problem to break down for d since to get rid of the square root I have to times everything then I'll end up with a d to powers of 1 2 3 and 4... I don't know how to solve that.

I'm only 6 days into this class.
 
Remember, you can combine trigonometric expressions. You don't necessarily have to substitute in for both sin and cos.
Also, you should have gone over solving higher degree polynomials in precalc. What's the highest math you've taken?
 
JeeebeZ said:
So,

cosθ = (1.5 - d) / 1.5

sinθ = √(1.52 - (1.5 - d)2) / 1.5

which would leave me with

60 / √(1.52 - (1.5 - d)2) = 200d / (1.5 - d)

What seems like a really hard problem to break down for d since to get rid of the square root I have to times everything then I'll end up with a d to powers of 1 2 3 and 4... I don't know how to solve that.

I'm only 6 days into this class.
Flip it over, square both sides.

Maybe I'm not seeing something, but it looks like a quadratic equation to me.
 

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