Statics Problem, two disks in equilibrium

[leomclaughlin]

Homework Statement

http://imgur.com/yVOXkAT

The two disks each have a mass of 18kg and are attached at their centers by an elastic cord that has a stiffness of k = 1.6kN/m . Determine the stretch of the cord when the system is in equilibrium and the angle θ of the cord. (Figure 1)

Homework Equations

F_x=0
F_y=0

The Attempt at a Solution

So far I've determined that the forces in the X-direction equals zero so cos(theta)lengthk=294.34(horizontal force of the left disk)
and in the y-direction,
sin(theta)lengthk=176.58(the y force of the right disk)
I believe this to be all I need, but I'm having trouble solving two equations with a sin and cos, and even then I'm not entirely sure if my calculations are correct. Any help is appreciated.

 

[mfb]

"length" should get its own variable instead of a word (the sketch uses l).
You can solve for l*k in one equation and use this in the other. Alternatively (and quicker), divide one equation by the other.

 

[nil1996]

According to me finding tension in the cord would work good.Once you get the tension you can easily find the extension.

 

[leomclaughlin]

well i was wrong, if i divide the equations by each other to get tan(theta)=.6, solving for theta gives me 30.96, which ironically is the lower left angle of the triangle, and its incorrect. Now I'm not sure where to go from here

 

[leomclaughlin]

i was attempting to find the tension in the cord by splitting it into its x and y components, from there I could solve for length and theta, or take the x and y components and use Pythagoreans theorem to get the hypotenuse?

 

[haruspex]

"length" should get its own variable instead of a word (the sketch uses l).
You can solve for l*k in one equation and use this in the other. Alternatively (and quicker), divide one equation by the other.

The length, x, to use in the T = kx equation is the extension of the cord, which will be rather less than l. The tension needs to be calculated from the FBDs of the discs, and the extension deduced from that.

 

[mfb]

Ah right, l is the rest length. Okay, that makes more sense.

 

[haruspex]

Ah right, l is the rest length. Okay, that makes more sense.

No, from the diagram I think l is the extended length, but how that's made up of rest length and extension is unknown.

 

[leomclaughlin]

So is it impossible to answer because I was not given a rest length of the cord? Everyone is mentioning variable without a whole lot of focus on the problem at hand. The only horizontal force is that which the left disk provides, so the cosine of the string theta multiplied by k and stretched length l should equal the horizontal force provided by the left disk, but that is one equation and two unknowns. The other equation would be the sin of the string theta * l*k equals the vertical component of both disks I believe

 

[haruspex]

So is it impossible to answer because I was not given a rest length of the cord? Everyone is mentioning variable without a whole lot of focus on the problem at hand. The only horizontal force is that which the left disk provides, so the cosine of the string theta multiplied by k and stretched length l should equal the horizontal force provided by the left disk, but that is one equation and two unknowns. The other equation would be the sin of the string theta * l*k equals the vertical component of both disks I believe

Don't worry about the stretching of the cord for the moment. Just treat it as a string of known length under unknown tension T. There is also its unknown angle and two unknown normal forces. You can write down four equations concerning the horizontal and vertical forces at the discs. Solve to find T.