Question

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

Answer 1

Vertical component =  2.25 N downward

Horizontal component = 1.05 N to the right

Magnitude of the net force = √ (2.25² + 1.05²)
                                              = √6.165 =              2.483 N  (rounded)

Direction of the net force = tan⁻¹ (1.05/2.25) to the right of downward

                                           = tan⁻¹ ( 7/15 ) to the right of downward

                                           = 25° to the right of downward (rounded)

Answer 2

The magnitude of the net force on the apple is $\boxed{2.48{\text{ N}}}$.

The direction of the net force is with vertical $\boxed{25^\circ}$.

Further explanation:

Here, we have to calculate the magnitude and the direction of the net force on the apple.

Given:

The gravitational force exerted on the apple is $2.25{\text{ N}}$.

Force exerted by the wind on the apple is $1.05{\text{ N}}$.

Formula and concept used:

The gravitational force is a universal force and it act in downward direction that is towards the center of the earth.

The direction of the force exerted by the wind on the apple is towards write side in the horizontal direction.

So, the angle between the gravitational force and force due to wind will be $90^\circ$ that is both the forces are perpendicular to each other.

Consider gravitational force is $W$ and force due to wind is $F$.

So, the net force applied on the apple is,

$\boxed{R=\sqrt {\left( {{W^2} + {F^2} + 2WF\cos \theta } \right)} }$

Here, $\theta$ is the angle between both the forces which is equal to the $90^\circ$.

So, the above equation can be written as,

$R=\sqrt {{W^2} + {F^2}}$                                                                                   …… (1)

The direction of the net force can be written as,

$\boxed{\phi={{\tan }^{ - 1}}\left( {\frac{F}{W}}\right)}$                                  ….. (2)

Calculation:

Substitute $2.25{\text{ N}}$ for $W$ and $1.05{\text{ N}}$ for $F$ in the equation (1).

$\begin{aligned}R&=\sqrt {{{2.25}^2}+{{1.05}^2}}\\&=\sqrt {6.165}\\&=2.48{\text{ N}}\\\end{gathered}$

For the direction,

Substitute $2.25{\text{ N}}$ for $W$ and $1.05{\text{ N}}$ for $F$ in the equation (2).

$\begin{aligned}\phi&={\tan ^{ - 1}}\left( {\frac{{1.05}}{{2.25}}} \right)\\&=25^\circ\\\end{aligned}$

Thus, the net force on the apple is $\boxed{2.48{\text{ N}}}$ and direction of the net force is with vertical $\boxed{25^\circ}$.

Learn more:

1. Water is a compound: brainly.com/question/1073452

2. Expansion of the gas with change in temperature: brainly.com/question/9979757

3. Two arrows are fired simultaneously with the speed of 30m/s brainly.com/question/2370982

Answer detail:

Grade: Senior School

Subject: Physics

Chapter: Force

Keywords:

Wind blow, apple falls, gravitational force, wind force, magnitude of force, direction of force, 2.25N downward, 1.05N, magnitude and direction, net force on apple.