Determine mDetermine the magnitude of the force that rope 1 exerts on the knot.Determine the magnitude of the force that rope 3 exerts on the knot. **Text Transcription:**You hang a light in front of your house using an elaborate system to keep the light in static equilibrium (Figure 1) with θ₂ = 50° and θ₃ = 0°. Rope 2 is found to exert a 100-N force on the knot.**Figure Explanation:**The diagram shows a system with three ropes. - **Rope 1** is vertical, attached to a mass labeled "m," indicating it holds the weight of the object.- **Rope 2** is inclined at an angle θ₂ = 50° to the horizontal, applying a 100-N force at the knot where the ropes meet.- **Rope 3** is horizontal with an angle θ₃ = 0°. The intersection of the ropes is at a single point or knot, and the forces cause the mass "m" to remain in static equilibrium.

Given:- The mass of the Rope 2 is found to exert a 100-N force on the knot. T2 = 100 N θ2= 50°θ3= 0° Find:- a) Determine m b) Determine the magnitude of the force that rope 1 exerts on the knot. c) Determine the magnitude of the force that rope 3 exerts on the knot. a) We know that the mass of the object is given from the diagram as T2sinθ2= T1= mg 100sin50=mg m = 100sin(50)9.8m = 7.816kg The mass of the object is m = 7.816 kg b) The magnitude of the force that rope 1 exerts on the knot is given as T1= mg = 7.816×9.8T2= 76.597≈76.60T1= 76.60 N So the magnitude of the force that rope 1 exerts on the knot is 76.60 N c) The magnitude of the force that rope 3 exerts on the knot is given as T3cosθ3=T1T3= 76.60cos 0T3= 76.601T3= 76.60 N The magnitude of the force that rope 3 exerts on the knot is 76.60 N