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

`74.31\ \text{N}`

`16.59^(\circ)`

Step-by-step explanation:

P = 50 N

Q = 30 N

`\theta` = Angle between the vectors =
`45^(\circ)`

Resultant is given by

`R=√(P^2+Q^2+2PQ\cos\theta)\\\Rightarrow R=\sqrt{50^2+30^2+2* 50* 30* \cos45^(\circ)}\\\Rightarrow R=74.31\ \text{N}`

Angle of resultant

`\phi=\tan^(-1)(Q\sin\theta)/(P+Q\cos\theta)\\\Rightarrow \phi=\tan^(-1)(30* \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)`