The problem you're working on involves determining the $x$-component of the object's acceleration, given several forces acting on it. Let’s break down the steps to solve it.

Step 1: Identify the forces acting in the $x$-direction.

From the diagram:

• A 5.0 N force is acting at an angle of 20° from the horizontal.
• A 1.0 N force is acting directly along the positive $x$-axis.
• The 3.0 N force is acting straight downward, which does not contribute to the $x$-direction.
• The 2.82 N force is acting straight upward, so it also doesn't contribute to the $x$-component.

Step 2: Break the forces into components.

For the 5.0 N force at a 20° angle, we need to find its $x$-component: $F_{x,5.0N} = 5.0 \, \text{N} \times \cos(20^\circ)$ $F_{x,5.0N} \approx 5.0 \times 0.9397 = 4.6985 \, \text{N}$

Now, add the 1.0 N force along the $x$-axis, since it is already in the $x$-direction: $F_{x,\text{total}} = 4.6985 \, \text{N} + 1.0 \, \text{N} = 5.6985 \, \text{N}$

Step 3: Apply Newton’s Second Law.

The sum of forces in the $x$-direction gives the $x$-component of the acceleration: $\Sigma F_x = m a_x$ where $m$ is the mass of the object. The object’s acceleration in the $x$-direction can be found by rearranging the equation: $a_x = \frac{\Sigma F_x}{m}$

However, the mass $m$ isn’t provided explicitly in the problem. Assuming it's meant to be calculated from additional data not shown here, or if you have this data available, we can plug in the values to find the correct acceleration.

Questions:

1. Do you have the mass of the object to finalize the acceleration calculation?
2. Does the diagram provide more data on friction or other forces acting on the object?
3. Can we clarify if the acceleration was calculated using a mass different than expected?
4. Have you tried recalculating the trigonometric components to ensure correct input?
5. Do you want to solve for the $y$-component of acceleration as well?

Tip:

Make sure that all angles and forces are carefully accounted for when resolving components. Misreading an angle or missing a force can lead to significant errors.