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

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

Step-by-step 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=√(F_g^2+F_w^2+2F_gF_wcos\theta)\\\Rightarrow F=√(2.25^2+1.05^2+2* 2.25* 1.05* cos90)\\\Rightarrow F=2.48294\ N`

The angle between the resultant and the gravitational force would be

`tan^(-1)(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