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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

The image you uploaded shows two forces, \( F_2 \) and \( F_3 \), acting on an object with a given mass of 18.5 kg. The angle between the forces is 120°. You also provided the magnitudes of the forces:

- \( F_1 = 10.2 \, \text{N} \)
- \( F_2 = 16 \, \text{N} \)

We need to calculate the resultant force \( F_R \) and then use Newton's second law to determine the acceleration of the object.

### Step 1: Find the resultant force
The resultant force \( F_R \) can be calculated using the law of cosines:

\[
F_R = \sqrt{F_1^2 + F_2^2 + 2 \cdot F_1 \cdot F_2 \cdot \cos(\theta)}
\]
where \( \theta = 120^\circ \).

### Step 2: Use Newton's second law
Once we have the resultant force, we can find the acceleration using:

\[
a = \frac{F_R}{m}
\]

where \( m = 18.5 \, \text{kg} \).

Let me compute the values.The resultant force acting on the object is approximately \( 14.03 \, \text{N} \). Using this, the acceleration of the object is approximately \( 0.76 \, \text{m/s}^2 \).

Would you like more details on any part of this solution? Here are some related questions for further exploration:

1. How is the law of cosines applied to calculate the resultant force between two vectors?
2. What is the significance of the angle between forces in determining the resultant?
3. How would the acceleration change if the mass of the object was doubled?
4. What would the acceleration be if the angle between the forces was 90° instead of 120°?
5. How can vector components be used to calculate the resultant force in an alternative method?

**Tip:** When dealing with forces acting at angles, vector decomposition can sometimes simplify calculations by breaking forces into their horizontal and vertical components.

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

This problem demonstrates how to calculate the acceleration of an 18.5 kg object subjected to two forces, F1 = 10.2 N and F2 = 16 N, acting at an angle of 120°. Using vector addition and Newton's second law, you will learn how to find the resultant force and the corresponding acceleration. Suitable for students in Grades 9-12.

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