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

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To calculate the tension in the rope with a person at the midpoint, the mass of the person (47 kg) and the sag of the rope (10.0) are key factors. The tension can be derived using the equilibrium of forces, where the sum of vertical forces equals zero, incorporating the weight of the person and the vertical component of tension. The horizontal component of tension can be found using the angle created by the sagging rope. By resolving these components, the total tension in the rope can be determined. This approach effectively combines the principles of static equilibrium and vector resolution.
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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
 
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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 verticle and horizontal directions must equal zero. Start by summing forces in the verticle 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.
 

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