Question

"Giant Swing", the seat is connected to two cables as shown in the figure (Figure 1) , one of which is horizontal. The seat swings in a horizontal circle at a rate of 37.0 rev/min .

Answer 1

The horizontal force is m*v²/Lh, where m is the total mass. The vertical force is the total weight (233 + 840)N. 

Fx = [(233 + 840)/g]*v²/7.5 

v = 32.3*2*π*7.5/60 m/s = 25.37 m/s 

The horizontal component of force from the cables is Th + Ti*sin40º and the vertical component of force from the cable is Ta*cos40º 

Thh horizontal and vertical forces must balance each other. First the vertical components: 

233 + 840 = Ti*cos40º 

solve for Ti. (This is the answer to the part b) 

Horizontally 

[(233 + 840)/g]*v²/7.5 = Th + Ti*sin40º 

Solve for Th 

Th = [(233 + 840)/g]*v²/7.5 - Ti*sin40º 

using v and Ti computed above.