How Do You Calculate the Tension in a Rope with a Person Midway Across?

[chica-88]

Homework Statement

Arlene is to walk across a "high wire" strung horizontally between two buildings 10.0 apart. The sag in the rope when she is at the midpoint is 10.0 , as shown in the figure .

If her mass is 47.0 , what is the tension in the rope at this point?

Homework Equations

Tension=ma

The Attempt at a Solution

I know that the mass is 47 kg but I don't know how to find the acceleration or if I am even using the correct formula. Please help

 

[kjohnson]

F=ma is the correct formula to use but there is no acceleration present so the right hand side is zero. The left hand side is the sum of the forces on the person (tension and weight). Thus the sum of the forces in the vertical and horizontal directions must equal zero. Start by summing forces in the vertical which will allow you to solve for your "y" component of tension. Then use the given angle of the rope to calculate the "x" component of tension. Then its just determine the resultant total tension.