# Minimize the Tension

1. Oct 31, 2009

### munchy35

1. The problem statement, all variables and given/known data

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,

2. Oct 31, 2009

### 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.

3. Nov 1, 2009

### 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

4. Nov 1, 2009

### tiny-tim

Hi munchy35!
Nooo … stop trying to take short-cuts!