In a two-dimensional tug-of-war, Alex, Betty, and Charles pull on ropes that are

Question

In a two-dimensional tug-of-war, Alex, Betty, and Charles pull on ropes that are tied to an automobile tire. The ropes make angle with each other as shown in Figure 3.10, Part (a), which is a bird's eye view of the situation. Alex pulls with a force FA (220 N), while Charles exerts a force Fc (170 N). What force, Fg, does Betty apply to the system? The tire is stationary and the orientation of Charles' rope is not specified, i.e the angular direction, theta must also be determined. The three forces acting on the tire, as shown in Part (a), are described by the free-body diagram of the system in Part (b).

Explanation / Answer

let the force between Betty and Charlie be 90+

so in the traingle, the net vertical force = 0,

so now use Summation Y = 0

i.e TB cos theta = TC

so 220 cos47=170 cos theta

cos theta = 0.882

theta = 28.04 deg

since net horizontal force = 0

so force due to betty = 220 sin 47 + 170 sin 28.04

F due to Betty = 240.8 N ------<<<<<<<<<<<Answer

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