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What is the x component of the acceleration in m/s^2

To calculate the x-component of the acceleration of the body, we need to break down the forces into their x and y components, apply Newton's second law \( F = ma \), and focus on the x-direction.

### Given dataTo calculate the x-component of the acceleration of the body, we need to break down the forces into their x and y components, apply Newton's second law \( F = ma \), and focus on the x-direction.

### Given 
- Mass of the body, \( m = 2.83 \, \text{kg} \)
- Force magnitudes:
  - \( F_1 = 67.9 \, \text{N} \)
  - \( F_2 = 26.7 \, \text{N} \)
  - \( F_3 = 71.5 \, \text{N} \)
  
- Angles:
  - \( \theta = 43^\circ \) (angle of \( F_1 \) above the x-axis)
  - \( \phi = 22.1^\circ \) (angle of \( F_2 \) below the x-axis)

### Step 1: Resolve forces into their x-components

#### \( F_1 \):
The x-component of \( F_1 \) is:
\[
F_{1x} = F_1 \cos(\theta) = 67.9 \cos(43^\circ)
\]

#### \( F_2 \):
The x-component of \( F_2 \) is:
\[
F_{2x} = F_2 \cos(\phi) = 26.7 \cos(22.1^\circ)
\]

#### \( F_3 \):
\( F_3 \) is acting entirely in the negative x-direction (since it is horizontal), so:
\[
F_{3x} = - F_3 = -71.5 \, \text{N}
\]

### Step 2: Apply Newton's Second Law in the x-direction
Net force in the x-direction:
\[
F_{\text{net, x}} = F_{1x} + F_{2x} + F_{3x}
\]

The x-component of acceleration is:
\[
a_x = \frac{F_{\text{net, x}}}{m}
\]

Let me calculate the values next.The x-component of the acceleration is approximately \( 1.02 \, \text{m/s}^2 \).

Would you like further details on this or have any other questions?

Here are 5 related questions to expand on this problem:
1. How do we calculate the y-component of the acceleration?
2. How do angles impact the force components in different directions?
3. What is the net force in the y-direction?
4. How does the velocity at \( t = 0 \) affect the future motion of the object?
5. How would the results change if the mass of the object were different?

**Tip**: When resolving forces, always ensure to properly identify the direction and sign of each component (positive or negative).

What is the x component of the acceleration in m/s^2?

This problem involves calculating the x-component of acceleration for a body using Newton's Second Law and vector decomposition. Forces F1 = 67.9 N, F2 = 26.7 N, and F3 = 71.5 N are applied to a 2.83 kg body at specific angles. Learn how to resolve forces into components and apply F = ma.

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