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A tree limb of mass 12 kg falls straight down. If air resistance exerts 27 N of force on the limb as it falls, what is the net force on the tree limb?

A. 118 N down
B. 27 N down
C. 15 N down
D. 91 N down

Answer :

[tex]Given:\\m=12kg\\g=9.81 \frac{m}{s^2} \\|\overrightarrow{F_a}|=27N\\\\Find:\\|\overrightarrow{F_n}|=?\\\\Solution:\\\\\overrightarrow{F_n}=\overrightarrow{F_a}+\overrightarrow{F_c}\\\\|\overrightarrow{F_c}|=mg\\\\\overrightarrow{F_a}\uparrow\;\;\;\land\;\;\;\overrightarrow{F_c}\downarrow\;\;\;\Rightarrow |\overrightarrow{F_n}|=|\overrightarrow{F_a}|-|\overrightarrow{F_c}|\\\\ |\overrightarrow{F_n}|=|\overrightarrow{F_a}|-mg\\\\|\overrightarrow{F_a}|=27N-12kg\cdot 9.81 \frac{m}{s^2}\approx -91N\\\\|\overrightarrow{F_n}|<0\Rightarrow \overrightarrow{F_n}\downarrow \\\\Correct\; is \;answer \;D[/tex]

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Rewritten by : Barada

The net force on the tree limb is 91 N. Option (D) is correct.

What is force?

The definition of force in physics is: The push or pull on a mass-containing item changes its velocity.

An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude. A spring balance can be used to calculate the Force. Newton is the SI unit of force.

Given parameters:

Mass of the tree limb: m = 12 kg.

Force exerts by air resistance: f = 21 N.

We know that: acceleration due to gravity: g = 9.8 m/s².

Weight of the tree limb is: W = mg = 12 kg × 9.8 m/s² = 117.6 N.

As force exerts by air resistance and weight of the tree limb acts in opposite direction, the net force on the tree limb is = W - f

= 117.6 N - 21 N

= 90.6 N

=91 N.

Learn more about force here:

https://brainly.com/question/13191643

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