Question

Using a scale of 1 cm to represent 10 N, find the size and direction of the resultant of forces of 50 N
and 30 N acting at the angle of 45 O to each other.

Answer 1

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 $16.59^{\circ}$