Question

A gust of wind blows an apple from a tree. As the apple falls, the gravita- tional force on the apple is 2.25 N downward, and the force of the wind on the apple is 1.05 N to the right.
Find the magnitude and direction of the net force on the apple.

Answer 1

Answer:

The magnitude of the net force is 2.48294 N and the angle is 25.02° with respect to the vertical

Explanation:

Consider the gravitational force as $\vec{F_g}=2.25\ N$

Consider the wind force as $\vec{F_w}=1.05\ N$

The angle between the gravitational force and wind force is 90°

From the parallelogram law we have

$F=\sqrt{F_g^2+F_w^2+2F_gF_wcos\theta}\\\Rightarrow F=\sqrt{2.25^2+1.05^2+2\times 2.25\times 1.05\times cos90}\\\Rightarrow F=2.48294\ N$

The angle between the resultant and the gravitational force would be

$tan^{-1}\frac{1.05}{2.25}=25.02^{\circ}$

The magnitude of the net force is 2.48294 N and the angle is 25.02° with respect to the vertical