A car is being pulled out of the mud by two forces that are applied by the two r

Question

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 = 28.0° angle. The magnitude of the force applied by each rope is 2600 newtons. Arrange the force vectors tail to head and use the graphical technique to answer the following questions.

(a) How much force would a single rope need to apply to accomplish the same effect as the two forces added together? ________N

(b) How would the single rope be directed relative to the dashed line?

along the dashed line

Aalong the dashed line

Bnot enough information to decide    

Cslightly below the dashed line

Dperpendicular to the dashed line

Explanation / Answer

If you add the two vectors head to tail you will see that the "vertical" parts (parts pulling perpendicular to the car) cancel out, since one is going down and one is up at the same angle. So to find the total force, we just need to add the parts that are pulling parallel to the car. So:

2600*Cos(13o) + 2600*Cos(-13o) = 5066.72 N

[Note: this is the same as twice one of them - 2*2600*Cos(13o) ]

So to do the same work as the two ropes, a single rope would have to pull with a force of 5066.72 N right along the dashed line so that all of the force goes into accelerating the car linear (and not turning it).

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