Let's analyze the problem step by step from the uploaded image. It contains several scenarios involving Newton's second law ($F = ma$) and requires calculating net force ($\Sigma F$) and acceleration ($a$).

Breakdown of Each Question

1. Scenario 1: A box lies at rest on a table.

   • Here, no net force ($\Sigma F$) acts on the box since it's stationary.
   • $\Sigma F = 0 \, \text{N}$, and thus, $a = 0 \, \text{m/s}^2$.

2. Scenario 2: A 2-kg box is free-falling to the ground.

   • Only the force of gravity acts on the box: $\Sigma F = F_{\text{gravity}} = m \cdot g = 2 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 19.6 \, \text{N}.$
   • Acceleration ($a$) is: $a = g = 9.8 \, \text{m/s}^2 \, \text{(since only gravity acts)}.$

3. Scenario 3: A 3-kg box with a parachute falls through the air at constant speed.

   • Since the box moves at constant speed, net force ($\Sigma F$) is zero: $\Sigma F = 0 \, \text{N}.$
   • Acceleration ($a$) is: $a = 0 \, \text{m/s}^2 \, \text{(no change in velocity)}.$

4. Scenario 4: A 4-kg box accelerates upward as it falls, due to air resistance of 80 N.

   • Force of gravity: $F_{\text{gravity}} = m \cdot g = 4 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 39.2 \, \text{N}.$
   • Net force ($\Sigma F$): $\Sigma F = F_{\text{air resistance}} - F_{\text{gravity}} = 80 \, \text{N} - 39.2 \, \text{N} = 40.8 \, \text{N}.$
   • Acceleration ($a$): $a = \frac{\Sigma F}{m} = \frac{40.8 \, \text{N}}{4 \, \text{kg}} = 10.2 \, \text{m/s}^2.$

5. Scenario 5: A 3-kg box slides to the right across a table with no applied force; friction = 5 N.

   • Friction is the only force acting, so: $\Sigma F = -F_{\text{friction}} = -5 \, \text{N}.$
   • Acceleration ($a$): $a = \frac{\Sigma F}{m} = \frac{-5 \, \text{N}}{3 \, \text{kg}} = -1.67 \, \text{m/s}^2.$

Would you like further clarification or step-by-step explanation for any specific scenario?

Follow-Up Questions

1. Why is acceleration zero when an object moves at constant speed?
2. How does air resistance affect free-falling objects?
3. Can you identify other scenarios where net force equals zero?
4. What factors influence the force of friction in Scenario 5?
5. How does Newton's second law apply to real-world applications like car acceleration?

Tip

Always consider the direction of forces when calculating the net force ($\Sigma F$). Use positive and negative signs to reflect their opposing directions.