Question

find fnorm of the block using the provided diagram. fgrav = 284 n fapp = 52 n a = 3.2 m/s^2

Explanation:

Step1: Analyze vertical forces

In the vertical direction, the normal force \(F_{\text{norm}}\) and the gravitational force \(F_{\text{grav}}\) act on the block.

Step2: Apply Newton's second law in vertical direction

Since there is no acceleration in the vertical direction (\(a_y = 0\)), according to Newton's second law \(F_{net,y}=ma_y\). The net force in the vertical direction \(F_{net,y}=F_{\text{norm}}-F_{\text{grav}}\).
Since \(a_y = 0\), then \(F_{net,y}=0\). So \(F_{\text{norm}}-F_{\text{grav}} = 0\).

Step3: Solve for \(F_{\text{norm}}\)

We can rearrange the equation \(F_{\text{norm}}-F_{\text{grav}} = 0\) to get \(F_{\text{norm}}=F_{\text{grav}}\). Given \(F_{\text{grav}} = 284\ \text{N}\), so \(F_{\text{norm}}=284\ \text{N}\). The applied force \(F_{\text{app}}\) and acceleration \(a = 3.2\ \text{m/s}^2\) (which is in the horizontal direction) do not affect the normal force calculation in the vertical direction as there is no vertical acceleration.

Answer:

$284\ \text{N}$