How Do You Calculate Tension in a Hammock's Ropes?

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To calculate the tension in a hammock's ropes, the weight of the person (51.0 kg) must be balanced by the vertical components of the tension in the ropes, which are at a 19.0-degree angle. The equation used is tsin(theta) + tsin(theta) - mg = 0, where m is the mass and g is the acceleration due to gravity (9.8 m/s²). The correct formula for tension is t = (mg) / (2sin(theta)), leading to t = (51 * 9.8) / (2 * sin(19.0)). The initial attempt at solving this resulted in an incorrect value of 25 N due to a miscalculation. Properly applying the formula will yield the correct tension in the ropes.
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Homework Statement


A 51.0kg person takes a nap in a backyard hammock. Both ropes supporting the hammock are at an angle of 19.0 above the horizontal. Find the tension in the ropes.


Homework Equations


ty=tsin/theta
wy=-mg
possibly?

The Attempt at a Solution


tsin/theta+tsin/theta-mg=0
t=(51)(9.8)/2(sin19.0)
t=25...i know its wrong...someone help PLEASE, i don't understand anything my professor teaches so i can never apply anything. -_-
 
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stressedout09 said:

The Attempt at a Solution


tsin/theta+tsin/theta-mg=0
t=(51)(9.8)/2(sin19.0)
t=25...i know its wrong...
Perhaps you should use another bracket for the expression
t=(51)(9.8)/2(sin19.0)
t=(51)(9.8)/(2(sin19.0))
 

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