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In the given diagram, we have two masses, \( m_1 = 8 \, \text{kg} \) and \( m_2 = 2 \, m_1 = 16 \, \text{kg} \). There is also a force \( F = 50 \, \text{N} \) acting at an angle \( \alpha = 60^\circ \) on \( m_1 \), and it appears to be connected to \( m_2 \) through a pulley system.

### Steps to find \( N \), the normal force on \( m_1 \):

1. **Forces acting on \( m_1 \):**
   - Weight: \( W_1 = m_1 g = 8 \times 9.8 = 78.4 \, \text{N} \) downward.
   - Normal force: \( N \), which is the force exerted by the surface on \( m_1 \) (vertical and upward).
   - Force \( F = 50 \, \text{N} \) at an angle of \( \alpha = 60^\circ \) to the horizontal.

2. **Decomposing \( F \):**
   - The vertical component of \( F \) is \( F_{\text{vertical}} = F \sin \alpha = 50 \sin 60^\circ = 50 \times \frac{\sqrt{3}}{2} = 43.3 \, \text{N} \) upward.
   - The horizontal component is \( F_{\text{horizontal}} = F \cos \alpha = 50 \cos 60^\circ = 50 \times \frac{1}{2} = 25 \, \text{N} \) (but this component doesn't affect the normal force).

3. **Normal force calculation:**
   The normal force \( N \) will balance out the vertical forces acting on \( m_1 \). These forces are:
   - Downward: Weight of \( m_1 \), \( W_1 = 78.4 \, \text{N} \).
   - Upward: Vertical component of \( F \), which is \( F_{\text{vertical}} = 43.3 \, \text{N} \).

   Hence, the normal force can be found by balancing the vertical forces:
   \[
   N + 43.3 = 78.4
   \]
   Solving for \( N \):
   \[
   N = 78.4 - 43.3 = 35.1 \, \text{N}
   \]

Thus, the normal force \( N \) on \( m_1 \) is **35.1 N**.

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Do you want more details on the steps, or have any specific questions?

Here are 5 related questions to further expand:
1. How would friction affect the normal force if it were included in the problem?
2. What would change if the angle \( \alpha \) were different?
3. How can the tension in the string between \( m_1 \) and \( m_2 \) be calculated?
4. What is the acceleration of the system if the pulley is frictionless?
5. How would you approach the problem if the surface under \( m_1 \) were inclined?

**Tip**: Decomposing forces into vertical and horizontal components simplifies the analysis of forces acting on objects.

Learn how to calculate the normal force acting on a mass m1 under the influence of an angled force and a pulley system. This problem demonstrates the application of Newton's Laws of Motion, force decomposition, and the balance of vertical forces. Suitable for high school physics students in Grades 10-12.

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