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 $F$ with an angle $\theta$ to the horizontal is $F_x = F\cos\theta$. Here, $F = 65$ N and $\theta=58^{\circ}$. So, $F_x=65\times\cos(58^{\circ})$.
Since $\cos(58^{\circ})\approx0.5299$, then $F_x = 65\times0.5299\approx 34$ N. There is no other horizontal force as the surface is frictionless. So the net force in the x - direction is the x - component of the applied force.

Answer:

34 N