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).