Physics help is needed on hammock problem?
Find the tension in each of the two ropes supporting a hammock if one is at an angle of theta1= 19 above the horizontal and the other is at an angle of theta2= 37 above the horizontal. The person sleeping in the hammock (unconcerned about tensions and ropes) has a mass of 70 kg.
that doesnt work, itried using both equations
For this problem, you need two equations: one for the x-component and one for the y-component.
Let T1 = tension of the string at 19 degrees
Let T2 = tension of the string at 37 degrees
The y-component should be the forces acting in the vertical direction. In this case, it’s the weight of the person acting in one direction while the sine components of the rope are acting in the other direction. Since forces are balanced, mg = T1sin19 + T2sin37.
The x-component should be the forces acting in the horizontal direction. In this case, the cosine components of the ropes are acting in the opposite directions: one the left, the other the right. Since forces are balanced, T1cos19 = T2cos37.
Use the second equation to solve for one force in terms of the other, and plug that into the first equation. That should give you one force. To get the second one, just plug your answer into any of the two equations.
Hope that helps.
EDIT: You have to use the second equation to solve for one force. For example, T1 = T2cos37/cos19.
Then plug this into the original equation to get: mg = (T2cos37/cos19)sin19 + T2sin37.
Solve for T2.