We can write the work done by each person as:
W = F_horizontal * d
Since the work done by the husband and the wife is the same, we can write:
Fh_horizontal * d = Fw_horizontal * d
Where Fh_horizontal and Fw_horizontal are the horizontal components of the forces exerted by the husband and the wife, respectively. Since the distances d are the same, they cancel out, and we have:
Fh_horizontal = Fw_horizontal
Now we can find the horizontal components of the forces exerted by the husband and the wife using their angles with respect to the horizontal:
Fh_horizontal = Fh * cos(θh) = 67N * cos(58°)
Fw_horizontal = Fw * cos(θw) = Fw * cos(38°)
Now we can plug Fh_horizontal into the equation:
Fw * cos(38°) = 67N * cos(58°)
We want to find Fw, so we can rewrite this equation as:
Fw = (67N * cos(58°)) / cos(38°)
Now we can plug in the values for the angles:
Fw = (67N * cos(58°)) / cos(38°) = (67N * 0.529) / 0.788
Fw ≈ 45.1 N
So the magnitude of the pulling force exerted by the wife is approximately 45.1 N.
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 degrees above the horizontal, and the wife's pulling force is directed 38 degrees above the horizontal. The husband pulls with a force whose magnitude is 67N. What is the magnitude of the pulling force exerted by the wife?
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