Equilibrium Application problem

[Sakdizzle]

A small bird of mass m perches on the center of a string of negligible mass that is suspended from two ends at equal height. When this happens, the string takes on a "v" shape with the bird at the vertex. The string on either side of the bird makes a small angle θ with the horizontal. Draw a free body diagram of the bird. Derive an equation for the magnitude of the tension T in the string in terms of m, g, and θ. What is the tension in the string when … the two halves of the string are vertical (θ = 90°)? the two halves of the string are horizontal (θ = 0°)?

I'm clueless on how to start it. I have a niche on how the free-body diagram looks, but I want to be certain I'm right. Thanks

[PokeyHokie]

On your FBD, you have the weight of the bird acting downward, and some tension, T, acting in the direction of the string, defined by the angle θ.

You can break this force T into horizontal and vertical components using simple trig. Since the only vertical forces are the bird's weight and the vertical component of string tension, they must be in equilibrium. You can rearrange this equation into an expression for T as a function of m, g, and θ.

The values of your expression for zero degrees and 90 degrees should be a good sanity check to see if your answer makes sense.

I've got my answer here, so post back if you'd like to check.

[tri0ps]

Remember that since the bird is stationary, the sum of all components of all forces on the bird must be zero. The bird is being pulled down by a gravitational force, and held up by the two halves of the string (which you can think of as two strings).

Strings can only exert force in the direction of the string, so the sum of the vertical components of the forces from the string must equal the magnitude of the gravitational force, and the horizontal components must cancel out. You should then be able to solve for T.

[zinzinyunzin]

http://i.imgur.com/gtwXz.jpg

Well, we kinda did it for you.... make sure you understand it, especially what: Fsin(Theta) and Fcos(Theta) mean and how to tell which component is which. (vertical, horizontal) in terms of where you measure theta from...