a box is at rest on a ramp at an incline of 22°. the normal force on the box is 538 n. what is the…

Explanation:

Step1: Resolve forces on ramp

The normal force $N$ on a box on a ramp is related to the gravitational force $F_g$ by $N = F_g\cos\theta$, where $\theta$ is the angle of the incline. We need to solve for $F_g$.

Step2: Rearrange formula

Rearranging $N = F_g\cos\theta$ gives $F_g=\frac{N}{\cos\theta}$.

Step3: Substitute values

We know $N = 538$ N and $\theta = 22^{\circ}$. So $F_g=\frac{538}{\cos(22^{\circ})}$. Since $\cos(22^{\circ})\approx0.9272$, then $F_g=\frac{538}{0.9272}\approx580$ N.

Answer:

580 N