What Is the Magnitude of the Pulling Force Exerted by the Wife?

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SUMMARY

The discussion centers on calculating the magnitude of the pulling force exerted by a wife while pulling a wagon, given that the husband exerts a force of 66 N at an angle of 58° above the horizontal and the wife pulls at an angle of 34°. The work done by both is equal, leading to the equation 66 * cos(58) = FORCE * cos(34). By simplifying this equation, the magnitude of the wife's pulling force can be determined using the formula FORCE = 66 * cos(58) / cos(34).

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Homework Statement



A husband and wife take turns pulling their child in a wagon along a horizontal sidewalk. Each exerts a constant force and pulls the wagon through the same displacement. They do the same amount of work, but the husband's pulling force is directed 58° above the horizontal, while the wife's pulling force is directed 34° above the horizontal. The husband pills with a force whose magnitude is 66 N. What is the magnitude of the pulling force exerted by his wife?


Homework Equations





The Attempt at a Solution

 
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Any ideas on how to do this before we help?
 
w = f * d (vectors)

w of man = 66 * cos(58) * D

w of woman = force * cos(34) * D

w of woman = w of man

66 * cos(58) * D = FORCE * cos(34) * D

the distances cancel out and you are left with

66 * cos(58)/cos(34) = answer
 

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