To find the normal force ($F_n$) acting on the block, we need to analyze the forces acting in the vertical direction. Here’s a breakdown of the given information:

Known values:

• Mass of the block: $m = 89 \, \text{kg}$
• First applied force, $F_{\text{app1}} = 100.8 \, \text{N}$, directed at $130^\circ$ from the horizontal.
• Second applied force, $F_{\text{app2}} = 95.5 \, \text{N}$, directed at $30^\circ$ from the horizontal.
• Gravitational force ($F_g$) is the weight of the block: $F_g = mg = 89 \times 9.81 = 873.09 \, \text{N}$ downward.

Steps:

1. Vertical Components of Applied Forces:

   • $F_{\text{app1,y}} = F_{\text{app1}} \sin(130^\circ)$
   • $F_{\text{app2,y}} = F_{\text{app2}} \sin(30^\circ)$

2. Normal Force Calculation: The normal force will balance the forces in the vertical direction. The equation for vertical equilibrium is: $F_n + F_{\text{app1,y}} + F_{\text{app2,y}} = F_g$ We can rearrange this to find the normal force: $F_n = F_g - F_{\text{app1,y}} - F_{\text{app2,y}}$

Let’s calculate this now.The normal force $F_n$ acting on the block is approximately $748.12 \, \text{N}$.

Would you like more details or have any questions about this?

Here are 5 related questions for further exploration:

1. How would the normal force change if the angles of $F_{\text{app1}}$ and $F_{\text{app2}}$ were reversed?
2. What happens to the normal force if the mass of the block increases?
3. How would we calculate the frictional force if the coefficient of friction were provided?
4. What if $F_{\text{app1}}$ was applied horizontally? How would that affect the normal force?
5. How would the normal force be affected if the block were on an inclined plane?

Tip: Always resolve forces into their vertical and horizontal components when dealing with forces applied at angles.