Minimize Tension of Mass m Hanging from Cords

[munchy35]

Homework Statement

A package of mass m hangs from a short cord that is tied to the wall via cord 1 and to the ceiling via cord 2. Cord 1 is at angle 40 degrees with the horizontal; cord 2 is at angle, theta.

a) for what value of theta is the tension in cord 2 minimized?
b)in terms of mg, what is the minimum tension in cord 2?

(here's the link of the problem with the picture http://www.unc.edu/~rowan/phys26/P26recit/p26-12-b.htm )

I know I have to figure out the force diagram first. I'm just having trouble with where to start.

I'm not asking for the solution, i just need some direction,

 

[tiny-tim]

Hi munchy35!

You can solve this either with a vector triangle, or by taking components in a convenient direction.

Choose one method, and show us how far you get. ​

 

[munchy35]

i used the component method so

for horizontal component i said t1cos40=t2cosx

(i'm just using x for theta)

t2=t1cos40/cosx

and t1 = t2cosx/cos40

so for part a, i used the t2 equation and just assumed for t2 to be a minimum cos x had to be maximum, the maximum cosx=1, so x= 0 degrees

^ can i just assume that?

for part b, i used vertical component

t1sin40 + t2sinx = mg

after plugging in t1

t2 = mg/ tan40cos0 + sin0

and eventually get 1.192mg

is that right

 

[tiny-tim]

Hi munchy35!

… for horizontal component i said t1cos40=t2cosx
…
t1sin40 + t2sinx = mg
…
so for part a, i used the t2 equation and just assumed for t2 to be a minimum cos x had to be maximum, the maximum cosx=1, so x= 0 degrees

^ can i just assume that?

Nooo … stop trying to take short-cuts!

Your two equations are correct …

now eliminate t1 to find t2 …

then minimise t2.