Chapter 8, Problem 7P

* Kate joins Jim, Luis, and Adrienne in the rope-pulling exercise described in the previous two problems. This time, they tie four ropes to a ring. The three friends each pull on one rope, exerting the following forces: ${\stackrel{\to }{T}}_{1onR}\text{ (50 N}$ in the positive y-direction), $\stackrel{\to }{T_{2\text{ on R}}}(20N,25°$ above the negative x-axis), and ${\stackrel{\to }{T}}_{3onR}(70N$, $70°$ below the negative x-axis). Kate pulls rope 4, exerting a force ${\stackrel{\to }{T}}_{4onR}$

so that the ring remains in equilibrium, (a) Construct a force diagram for the ring, (b) Use the first condition of equilibrium to write two equations that can be used to determine $T_{4onRx}$: and $T_{4onRy}$. (c) Solve these equations and determine the —y magnitude and direction of ${\stackrel{\to }{T}}_{4onR}$.