Solving Mechanics Statics Homework Problem

[JeeebeZ]

Homework Statement

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

Homework Equations

The Attempt at a Solution

So I get that

ƩF_y = 0 = F_(rod)y - F_(weight)

ƩF_x = 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

 

[SammyS]

Homework Statement

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

Homework Equations

The Attempt at a Solution

So I get that

ƩF_y = 0 = F_(rod)y - F_(weight)

ƩF_x = 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 ?

 

[JeeebeZ]

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.

 

[runningninja]

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?

 

[SammyS]

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.