A home-built swing is suspended by a rope passing through two pulleys, and , whose ends meet at point where the swing is attached. The rope segments and make angles of and with the horizontal, respectively. When a child sits still on the seat, the tension in is 199 N. Given that, in this condition, the system is in equilibrium, find the combined weight of the child and the seat and the tension in the rope , giving your answers to the nearest two decimal places.
A particle is in equilibrium under the action of three coplanar forces of magnitudes N, 15 N, and 25 N. Given that the last two forces are perpendicular to each other, determine the value of .
The diagram shows a body weighing 6.1 N suspended in equilibrium by two light, inextensible strings, and . Given that , , and the strings are perpendicular, find the tensions and .