Question

a crate is pulled with a force of 165 n at an angle 30° northwest. what is the resultant horizontal force on the crate?
a 143 n
b 533 n
c 20 n
d 350 n

Explanation:

Step1: Resolve the force into horizontal component

We know that if a force $F$ is applied at an angle $\theta$ with respect to the horizontal - vertical axis, the horizontal component of the force $F_x$ is given by $F_x = F\cos\theta$. Here, $F = 165\ N$ and $\theta=30^{\circ}$, and the direction is northwest. The horizontal component of the force in the x - direction (assuming the standard coordinate system where north - south is along the y - axis and east - west is along the x - axis) is $F_x=-F\cos30^{\circ}$ (negative because it has a west - ward direction).
$F_x=- 165\times\frac{\sqrt{3}}{2}\approx - 143\ N$. The magnitude of the horizontal component of the force is approximately $143\ N$.

Answer:

A. $143\ N$