vertical component= F sin∅==> F sin45°==> 8 * (1/√2)==> 4√2 NewtonHorizontal component= F cos∅==> F cos45°==> 8 * (1/√2)==> 4√2 Newton

Resolving the Force
To resolve a force into its horizontal (x-axis) and vertical (y-axis) components, we use trigonometric functions. Given a force of 8 N at an angle of 45°, we can employ sine and cosine functions.
Step 1: Identify Components
- Horizontal Component (Fx):
- Formula: \( Fx = F \cdot \cos(\theta) \)
- Calculation: \( Fx = 8N \cdot \cos(45°) \)
- Vertical Component (Fy):
- Formula: \( Fy = F \cdot \sin(\theta) \)
- Calculation: \( Fy = 8N \cdot \sin(45°) \)
Step 2: Calculate Horizontal Component
- Using Cosine:
- \( \cos(45°) = \frac{\sqrt{2}}{2} \)
- \( Fx = 8N \cdot \frac{\sqrt{2}}{2} \)
- \( Fx = 8N \cdot 0.7071 \)
- \( Fx \approx 5.66N \)
Step 3: Calculate Vertical Component
- Using Sine:
- \( \sin(45°) = \frac{\sqrt{2}}{2} \)
- \( Fy = 8N \cdot \frac{\sqrt{2}}{2} \)
- \( Fy = 8N \cdot 0.7071 \)
- \( Fy \approx 5.66N \)
Final Results
- Horizontal Component (Fx):
- \( Fx \approx 5.66N \)
- Vertical Component (Fy):
- \( Fy \approx 5.66N \)
Summary of Components
- Horizontal Force (Fx): 5.66 N
- Vertical Force (Fy): 5.66 N
In conclusion, the force of 8 N at an angle of 45° resolves into horizontal and vertical components of approximately 5.66 N each. Understanding this resolution is crucial for analyzing forces in physics.