I need help with a specific problem:

A go-cart is being towed north by a car along a road with a net force of zero. The go-cart is attached to the car by two ropes. The tension in the ropes is the same, 31 N. The ropes make 22 degrees angles to the direction of motion, one on the west side and the other on the east. Determine the force of friction on the go-cart.

Fnet = 0, F1 = 31 N [N22W], F2 = 31 N [N22E]

The solutions show that to find Fx we use cos and to find Fy we use sine, but I thought it was the other way around (Fx is sine and Fy is cos).

Your help is greatly appreciated!

Sample Problem 2: Total Force of Friction on a Towed Object A go-carl is being towed north by a car along a road with a net For the x-component of the tension force, force of zero. The go-cart is attached to the car by two ropes. The tension in the ropes is the same, 31 N. The ropes make 22" angles to the direction of motion, one on the west side and = -(31 N) cos 22" the other on the east. Determine the force of friction on the Fix = -28.7 N (one extra digit carried) go-cart. Figure 8 shows a top view of the go-cart. The figure does not show the normal force and gravity because they are = (31 N) cos 22" perpendicular to the page and cancel each other. Far = 28.7 N (one extra digit carried) EF, = Fut Fit F Fur = EF, - (Fu + Ful =0 - (-28.7 N + 28.7 N) 32 27 F. = ON F. For the y-component of the tension force, Fir = Rising = (31 Njein 22 Fir = 116 N Fly = F, sine = (31 Njein 22 Figure U Far = 116 N Fly = EF, - (F + Fx) Given: XF = 0, K = 31 N [N 22" W]; $ = 31 N [N 22" =0 - 11.6N - 116N Required: force of friction on go-cart, F Fy = -23 N Analysis: Draw an FBD. There is no net force on the go-cart, Statement: The forces of the ropes in the a-direction cancel, so 30 EF, equals zero and 3 5, equals zero. The normal force and There is no force of friction in that direction. The force of friction the force of gravity cancel each other. Use F, = F cose and is 23 N [5)- F, = F sing to determine the components of the tension forces on the go-cart. To calculate the force of friction on the go-cart, use EF, = Fur+ Fast , and 35, = Fir+ For + Ry. Use north and east as the positive directions when determining components. Solution: The FOD is shown in Figure 9. Figure 9