Question

Part 1 :

A gust of wind blows an apple from a tree. As the apple falls, the force of gravity on the apple is 9.42N downward, and the force of the wind on the apple is 1.68N to the right.
What is the magnitude of the net external force on the apple? Answer in units of N.
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Part 2 :
What is the direction of the net external force on the apple (measured from the downward vertical, so that the angle to the right of downward is positive)? Answer in units of degrees.

Answer 1

The net external force acting on the apple is 9.57 N. The direction of this force is 10.09° to the right of the downward vertical.

Step-by-step explanation:

The magnitude of the net external force on the apple can be calculated using the Pythagorean theorem since the forces are acting at right angles to each other. The force of gravity (9.42 N) acts downward, and the force of the wind (1.68 N) acts to the right. The net force (Fnet) can be found by:

Fnet = √(F_gravity^2 + F_wind^2)

Fnet = √(9.42^2 + 1.68^2)

Fnet = √(88.7364 + 2.8224)

Fnet = √(91.5588)

Fnet = 9.57 N (rounded to two decimal places)

The direction of the net external force can be determined by calculating the angle to the horizontal using the tangent function:

tan(θ) = F_wind/F_gravity

tan(θ) = 1.68/9.42

• θ = atan(0.1783)
• θ = 10.09° (rounded to two decimal places)

This means the net external force is directed at an angle of 10.09° to the right of the downward vertical.

Answer 2

1) 9.57 N

We have two forces applied on the apple:

- The force of gravity, in the downward direction:

W = 9.42 N

- The force exerted by the wind, in the horizontal direction (to the right):

Fw = 1.68 N

The two forces are perpendicular to each other, so we can find the magnitude of the net force by using Pythagorean's theorem.

Therefore, we have:

`F=√(W^2+F_w^2)=√((9.42)^2+(1.68)^2)=9.57 N`

2)
`10^(\circ)`

The direction of the net external force, measured from the downward vertical, can be measured using the following formula:

`\theta = tan^(-1)((F_x)/(F_y))`

where

`F_x` is the force in the horizontal direction

`F_y` is the force in the vertical direction

In this problem,

`F_x = F_w = 1.68 N`

`F_y = W = 9.42 N`

and so we find:

`\theta = tan^(-1)((1.68)/(9.42))=10^(\circ)`