Question

a box is pulled to the right with a force of 65 n at an angle of 58 degrees to the horizontal. the surface is frictionless. the free body diagram is shown. what is the net force in the x - direction? 30 n 34 n 55 n 65 n

Explanation:

Step1: Resolve the applied force in x - direction

The formula for the x - component of a force $F$ at an angle $\theta$ with the horizontal is $F_x = F\cos\theta$. Here, $F = 65\ N$ and $\theta=58^{\circ}$.
$F_x=65\times\cos(58^{\circ})$

Step2: Calculate the value

We know that $\cos(58^{\circ})\approx0.5299$. So, $F_x = 65\times0.5299\approx 34\ N$. Since the surface is frictionless and there are no other horizontal forces, the net force in the x - direction is equal to the x - component of the applied force.

Answer:

34 N