Question

Forces of 9 lbs and 13 lbs act at a 38º angle to each other. Find the magnitude of the resultant force and the angle that the resultant makes with each force.

Answer 1

Explanation:

Answer 2

Answer:
`R=20.84\ lb\quad 22.57^(\circ),15.43^(\circ)`

Explanation:

Given

Two forces of 9 and 13 lbs acts
`38^(\circ)` angle to each other

The resultant of the two forces is given by

`\Rightarrow R=√(a^2+b^2+2ab\cos \theta)`

Insert the values

`\Rightarrow R=\sqrt{9^2+13^2+2(9)(13)\cos 38^(\circ)}\\\Rightarrow R=√(81+169+184.394)\\\Rightarrow R=√(434.394)\\\Rightarrow R=20.84\ lb`

Resultant makes an angle of

`\Rightarrow \alpha=\tan^(-1)\left( (b\sin \theta)/(a+b\cos \theta)\right)\\\\\text{Considering 9 lb force along the x-axis}\\\\\Rightarrow \alpha =\tan^(-1)\left( (13\sin 38^(\circ))/(9+13\cos 38^(\circ))\right)\\\\\Rightarrow \alpha =\tan^(-1)((8)/(19.244))\\\\\Rightarrow \alpha=22.57^(\circ)`

So, the resultant makes an angle of
`22.57^(\circ)` with 9 lb force

Angle made with 13 lb force is
`38^(\circ)-22.57^(\circ)=15.43^(\circ)`