Physics, 04.12.2019 06:31, Dweath50

The angle between the two force of magnitude 20n and 15n is 60 degrees (20n force being horizontal) determine the resultant in magnitude and direction

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answered: mia12340

The magnitude of the resultant is 30.4 N.

The resultant angle direction is 25.3°.

Explanation:

To find the resultant of the magnitude and direction for given forces “P” and “Q” are 20 N and 15 N respectively, the angle (θ) between them is 60°.

We know that from triangle law of forces,

$R=\sqrt{P^{2}+2 P Q \cos \theta+Q^{2}}$

Substitute the given values in the above formula,

$R=\sqrt{20^{2}+2 (20)(15) Q \cos 60+15^{2}}$

$R=\sqrt{400+600(0.5) + 225}$

$R=\sqrt{400+300 + 225}$

$R=\sqrt{925}$

R = 30.4 N

The magnitude of the resultant is 30.4 N.

To find the direction of the resultant we know that $\text {Resultant angle}=\tan ^{-1} \frac{Q \sin \theta}{P+Q \cos \theta}$

Substitute the given values in the above formula,

$\text {Resultant angle}=\tan ^{-1} \frac{15 \sin 60}{20+15 \cos 60}$

$\text {Resultant angle}=\tan ^{-1} \frac{12.99}{20+7.5}$

$\text {Resultant angle}=\tan ^{-1} \frac{12.99}{27.5}$

$\text { Resultant angle }=\tan ^{-1} 0.472$

Resultant angle=25.3°

The resultant angle direction is 25.3°.

answered: Guest

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answered: Guest

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