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las 2 fuerzas q se muestran en la figura  que actuan sobre un objeto de 18,5 kg . f1= 10,2N  , f2 = 16N halle su aceleracion de ellos

To solve the problem involving the two forces acting on an object of mass 18.5 kg, we need to calculate the net force acting on the object and then apply Newton's second law to find the acceleration.

### Given Data:
- \( F_1 = 10.2 \, N \) at an angle of \( 120^\circ \) relative to the positive \( x \)-axis.
- \( F_2 = 16.0 \, N \) along the positive \( y \)-axis.
- Mass of the object: \( m = 18.5 \, \text{kg} \).

### Steps:

1. **Resolve Forces into Components:**
   - \( F_1 \) has both \( x \)- and \( y \)-components because it is at an angle of \( 120^\circ \).
     - \( F_{1x} = F_1 \cos(120^\circ) \)
     - \( F_{1y} = F_1 \sin(120^\circ) \)
   - \( F_2 \) only acts along the \( y \)-axis:
     - \( F_{2x} = 0 \)
     - \( F_{2y} = 16.0 \, N \)

2. **Calculate Net Force in Each Direction:**
   - Net force in the \( x \)-direction: \( F_{\text{net},x} = F_{1x} + F_{2x} \)
   - Net force in the \( y \)-direction: \( F_{\text{net},y} = F_{1y} + F_{2y} \)

3. **Find Magnitude of the Net Force:**
   - Use the Pythagorean theorem to find the magnitude of the net force:
     \[
     F_{\text{net}} = \sqrt{F_{\text{net},x}^2 + F_{\text{net},y}^2}
     \]

4. **Apply Newton's Second Law to Find Acceleration:**
   \[
   a = \frac{F_{\text{net}}}{m}
   \]

Let me now calculate these values.### Solution:

1. **Force \( F_1 \) components:**
   - \( F_{1x} = -5.10 \, N \) (towards the negative \( x \)-direction)
   - \( F_{1y} = 8.83 \, N \) (positive \( y \)-direction)

2. **Net force components:**
   - \( F_{\text{net},x} = -5.10 \, N \) 
   - \( F_{\text{net},y} = 24.83 \, N \)

3. **Magnitude of the net force:**
   \[
   F_{\text{net}} = 25.35 \, N
   \]

4. **Acceleration:**
   \[
   a = \frac{25.35}{18.5} = 1.37 \, \text{m/s}^2
   \]

Thus, the acceleration of the object is approximately **1.37 m/s²**.

Would you like more details or clarifications? Here are five related questions you could explore:

1. How would the acceleration change if the mass of the object was doubled?
2. What would happen if the angle of \( F_1 \) were \( 90^\circ \) instead of \( 120^\circ \)?
3. Can you find the direction of the net force relative to the positive \( x \)-axis?
4. What role does the angle between forces play in determining the magnitude of the resultant force?
5. How would the acceleration change if only one force acted on the object?

**Tip:** When dealing with multiple forces, always resolve them into components along standard axes (e.g., \( x \)- and \( y \)-axes) for easier vector calculations.

las 2 fuerzas que se muestran en la figura que actúan sobre un objeto de 18,5 kg. F1 = 10,2 N, F2 = 16 N. Halle su aceleración.

This problem explores how to calculate the acceleration of an 18.5 kg object acted upon by two forces: F1 = 10.2 N at a 120° angle and F2 = 16 N along the y-axis. By resolving the forces into their components and applying Newton's second law, we determine the net force and acceleration. Suitable for high school physics students.

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