Resolving Forces in a Hanging Bag of Sand

[edsys89]

Homework Statement

A bag of sand weighing 100 N is hanging on the end of a long, light rope. The bag is pulled to one side by a horizontal force so that the rope makes an angle of 25⁰ with the vertical. Find the magnitudes of the horizontal force and the tension in the rope.

The Attempt at a Solution

I know that the horizontal force makes an angle of 115⁰ to the rope.
I know that the magnitude of the horizontal force + the force on the rope equal 100N.
I'm stuck on which way to go. Some sort of pendulum formula?

 

[HallsofIvy]

The bag still weighs 100N so there is a force of 100N straight down: that is -100 j. There is an unknown force Xi. The sum of those two forces is Xi- 100j and, because the only off setting force is the tension in the rope, at 25 degees with the vertical, if we call the tension "T", that vector is T sin(25)i- T cos(25)j. Set those equal and you have two equations to solve for X and T.

 

[PhanthomJay]

Homework Statement

A bag of sand weighing 100 N is hanging on the end of a long, light rope. The bag is pulled to one side by a horizontal force so that the rope makes an angle of 25⁰ with the vertical. Find the magnitudes of the horizontal force and the tension in the rope.

The Attempt at a Solution

I know that the magnitude of the horizontal force + the force on the rope equal 100N.

Why do you say this? Draw a free body diagram of the bag, identifying all forces acting on it, and the direction of those forces. Then apply Newton 1 in the x and y directions.