Question

Two forces act on an object. The first force has a magnitude of 360 newtons and acts at an angle of 30° as measured from the horizontal. The second force has a magnitude of 240 newtons and acts at an angle of 135° as measured from the horizontal. Determine the vector v that represents the resultant force.

Answer 1

Answer:377.46 N

Step-by-step explanation:

Given

Vector 1 has a magnitude of $360\ N$ and makes an angle of $30^{\circ}$

vector 2 has a magnitude of $240\ N$ and makes an angle of $135^{\circ}$

Net Horizontal force

$\sum F_h=360\cos 30+240\cos 135$

$\sum F_h=311.769-169.70$

$\sum F_h=142.069\ N\quad \ldots(i)$

Net vertical force

$\sum F_v=360\sin 30+240\sin 135$

$\sum F_v=180+169.705$

$\sum F_v=349.705\ N\quad \ldots(ii)$

Net resultant force

$F_{net}=\sqrt{F_h^2+F_v^2}$

$F_{net}=\sqrt{(142.069)^2+(349.705)^2}$

$F_{net}=377.46\ N$

angle which resultant make with x-axis

$\tan \theta =\frac{\sum F_v}{\sum F_h}$

$\tan \theta =\frac{349.705}{142.069}$

$\tan \theta =2.461$

$\theta =67.88^{\circ}$

Thus vector v is given by

$\vec{v}=377.46[\cos 67.88+\sin 67.88]$