Solving Mechanics Statics Homework Problem

In summary: Can you please break it down into a quadratic equation and then solve for d?In summary, the student is trying to solve for the equilibrium length of a spring, but is having difficulty due to the complexity of the problem.
  • #1
JeeebeZ
40
1

Homework Statement



http://s11.postimage.org/yvt7eeg35/image.png [Broken]

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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  • #2
JeeebeZ said:

Homework Statement



http://s11.postimage.org/yvt7eeg35/image.png [Broken]

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:
  • #3
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.
 
  • #4
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?
 
  • #5
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.
 

1. What is Statics in Mechanics?

Statics is a branch of mechanics that deals with the analysis of objects at rest or in a state of constant motion. It focuses on the study of forces and their effects on rigid bodies.

2. How do I approach solving a Mechanics Statics homework problem?

To solve a Mechanics Statics homework problem, it is important to first draw a free-body diagram of the object or system in question. Then, identify all the forces acting on the object and apply Newton's laws of motion to determine the resulting equilibrium equations.

3. What are the common types of problems in Mechanics Statics?

The most common types of problems in Mechanics Statics are equilibrium problems, which involve finding the forces acting on an object at rest, and truss problems, which involve analyzing the forces in a structure made up of interconnected beams or bars.

4. What are the key principles to keep in mind while solving Mechanics Statics problems?

The key principles to keep in mind while solving Mechanics Statics problems are the conservation of energy, the conservation of momentum, and the concept of equilibrium. It is also important to pay attention to the direction and magnitude of forces, and to use proper units in calculations.

5. What are some tips for successfully solving Mechanics Statics homework problems?

Some tips for successfully solving Mechanics Statics homework problems include practicing drawing accurate free-body diagrams, breaking down complex problems into smaller, more manageable parts, and double-checking all calculations and solutions. It is also helpful to seek clarification from a teacher or classmate if any concepts or steps are unclear.

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