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e-lub [12.9K]
3 years ago
12

Using a scale of 1 cm to represent 10 N, find the size and direction of the resultant of forces of 50 N

Physics
1 answer:
marta [7]3 years ago
4 0

Answer:

74.31\ \text{N}

16.59^{\circ}

Explanation:

P = 50 N

Q = 30 N

\theta = Angle between the vectors = 45^{\circ}

Resultant is given by

R=\sqrt{P^2+Q^2+2PQ\cos\theta}\\\Rightarrow R=\sqrt{50^2+30^2+2\times 50\times 30\times \cos45^{\circ}}\\\Rightarrow R=74.31\ \text{N}

Angle of resultant

\phi=\tan^{-1}\dfrac{Q\sin\theta}{P+Q\cos\theta}\\\Rightarrow \phi=\tan^{-1}\dfrac{30\times \sin45^{\circ}}{50+30\cos45^{\circ}}\\\Rightarrow \phi=16.59^{\circ}

Magnitude of the resultant is 74.31\ \text{N}

Direction of the resultant is 16.59^{\circ}

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