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What is the value of  ax
 , the  x
 -component of the object’s acceleration?



To find the \( x \)-component of the object's acceleration, we need to analyze the forces in the horizontal (x) direction, and then apply Newton's second law:

\[
F = ma
\]
where:
- \( F_x \) is the total force in the \( x \)-direction.
- \( m \) is the mass of the object.
- \( a_x \) is the \( x \)-component of acceleration.

Let's break down the forces in the \( x \)-direction based on the diagram:

### Forces in the \( x \)-direction:
1. **1.0 N**: This force is already along the positive \( x \)-axis, so it contributes \( +1.0 \, \text{N} \).
2. **5.0 N at an angle of 20°**: We need the \( x \)-component of this force. Using the cosine of the angle:
   \[
   F_{x, 5.0\,N} = 5.0 \cos(20^\circ)
   \]
3. **3.0 N**: This force is along the negative \( y \)-axis and does not have an \( x \)-component.

Adding these up gives the net force in the \( x \)-direction:
\[
F_x = 1.0 + 5.0 \cos(20^\circ)
\]
Once we have the total force, we can calculate the acceleration using \( F_x = ma_x \). However, to get the acceleration \( a_x \), we also need the mass \( m \) of the object, which is not provided in the diagram. If you have the mass, we can continue from there, but if it's not provided, we'll assume it's a known variable.

Let me know if you have the mass or if you'd like to clarify further!

---

Here are some questions that may help extend this:

1. What is the object's mass?
2. Do you need the \( y \)-component of the acceleration as well?
3. Should we calculate the net acceleration (magnitude and direction)?
4. Do you need a breakdown of the trigonometric components?
5. Would you like to know how to resolve forces in both axes?

**Tip:** Always resolve forces along each axis separately and then apply Newton's laws.

What is the value of ax, the x-component of the object’s acceleration?

Learn how to calculate the x-component of acceleration by resolving forces along the x-axis and applying Newton's second law. The problem involves trigonometry to break down forces and is suitable for students in Grades 11-12.

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