A car is being pulled out of the mud by two forces that are applied by the two ropes shown in the drawing.

A car is being pulled out of the mud by two forces that are applied by the two ropes shown in the drawing. The dashed line in the drawing bisects the 30.0° angle. Themagnitude of the force applied by each rope is 2900 newtons (N). (a) How much force would a single rope need to apply to accomplish the same effect as the two forcesadded together? (b) What angle would the single rope make relative to the dashed line?

Solutions

Expert Solution

The angle between the horizontal axis and the rope is

θ = 30 / 2
= 15
Each rope is making an angle 15 degree with the horizontal. The force applied by each rope is

F = 2900N cos 15( this is the horizontal component of force )
= 2801.2 N
if a single rope need to apply to accomplish the same effect then

T = 2 F

= 2 ( 2801.2)
= 5602.4N

genius_generous answered 2 years ago

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