To solve this problem, we’ll determine the net force ($\Sigma F$) and acceleration ($a$) acting on the object based on the forces provided in the image.

Step 1: Sum of Forces ($\Sigma F$)

The object is acted upon by two forces:

1. An upward force of $5 \, \text{N}$.
2. A downward force of $7.1 \, \text{N}$.

Since these forces act in opposite directions, we can calculate the net force by subtracting the upward force from the downward force:

$\Sigma F = 7.1 \, \text{N} - 5 \, \text{N} = 2.1 \, \text{N} \, (\text{downward})$

So, the net force acting on the object is $2.1 \, \text{N}$ in the downward direction.

Step 2: Acceleration ($a$)

Now, we can use Newton's second law to find the acceleration:

$\Sigma F = m \cdot a$

where:

• $m = 1.8 \, \text{kg}$
• $\Sigma F = 2.1 \, \text{N}$

Rearranging to solve for $a$:

$a = \frac{\Sigma F}{m} = \frac{2.1 \, \text{N}}{1.8 \, \text{kg}} = 1.167 \, \text{m/s}^2$

Final Answers:

• Net Force ($\Sigma F$) = $2.1 \, \text{N}$ (downward)
• Acceleration ($a$) = $1.167 \, \text{m/s}^2$ (downward)

Would you like further clarification on any step, or do you need additional help?

Relative Questions:

1. What is the significance of Newton's second law in calculating acceleration?
2. How would the acceleration change if the mass were different?
3. What would happen to the net force if both forces were in the same direction?
4. Can we determine velocity changes over time with just the net force and mass?
5. How would this problem differ if it involved frictional forces?

Tip: When forces act in opposite directions, always ensure to subtract the smaller force from the larger to get the net force and its direction.