A 51 kg gymnast hangs vertically from a pair of parallel rings.
(b) If the ropes are supported so that they make an angle of 35° with the ceiling, what is the tension in each rope?
A 51 kg gymnast hangs vertically from a pair of parallel rings.
(b) If the ropes are supported so that they make an angle of 35° with the ceiling, what is the tension in each rope?
Start with a Free-Body Diagram of the point where the three ropes meet. I have a +x axis horizontally to the right and a +y axis straight up. There is a tension T1 acting up and to the left making a 35 degree angle with the -x axis, there is a tension T2 acting up and to the right making a 35 degree angle with the +x axis, and there is a weight w acting straight down.
The point we have chosen is stationary and massless. So according to Newton's 2nd in the x-direction:
$\displaystyle \sum F_x = -T_1~cos(35) + T_2~cos(35) = 0$
So we know that $\displaystyle T_2 = T_1$. I'm just simply going to refer to this as "T" from now on.
In the y-direction we have:
$\displaystyle \sum F_y = T~sin(35) + T~sin(35) - w = 0$
Thus
$\displaystyle T = \frac{w}{2~sin(35)} = \frac{mg}{2~sin(35)}$
I'll let you pick up the rest.
-Dan