The image presents three scenarios where forces are applied to different objects, each with different masses and force configurations. We are tasked to determine which objects are not moving and which have the greatest acceleration.

Key points:

1. Newton's Second Law: $F = ma$, where $F$ is the net force acting on the object, $m$ is the mass, and $a$ is the acceleration.
2. Net Force Calculation: Net force is determined by subtracting the opposing forces applied on each object.
3. Acceleration: If the net force is zero, the object is not moving (acceleration = 0). If there is a net force, we calculate acceleration using $a = \frac{F_{net}}{m}$.

Let's go through the steps for each object:

(1) First Object:

• Mass: 5 kg

• Forces: $15 \, \text{N}$ to the right, $10 \, \text{N}$ and $5 \, \text{N}$ to the left.

  Net force: $F_{net} = 15 - (10 + 5) = 15 - 15 = 0 \, \text{N}$ Since $F_{net} = 0$, the object is not moving.

(2) Second Object:

• Mass: 3 kg

• Forces: $14 \, \text{N}$ to the left, $8 \, \text{N}$ and $10 \, \text{N}$ to the right.

  Net force: $F_{net} = (10 + 8) - 14 = 18 - 14 = 4 \, \text{N}$ Acceleration: $a = \frac{F_{net}}{m} = \frac{4}{3} \, \text{m/s}^2 \approx 1.33 \, \text{m/s}^2$

(3) Third Object:

• Mass: 2 kg

• Forces: $15 \, \text{N}$ to the right, $10 \, \text{N}$ and $5 \, \text{N}$ to the left.

  Net force: $F_{net} = 15 - (10 + 5) = 15 - 15 = 0 \, \text{N}$ Since $F_{net} = 0$, the object is not moving.

Conclusion:

• Not moving: Object 1 and Object 3 (net force is zero).
• Greatest acceleration: Object 2 (acceleration ≈ 1.33 m/s²).

Thus, the correct answer is 1 and 3.

Would you like further details or have any other questions?

Here are five related questions:

1. How do we calculate net force when forces are applied in opposite directions?
2. What happens to the acceleration if the net force is zero?
3. How does mass affect the acceleration of an object given the same net force?
4. Can friction affect these types of problems, and how would we account for it?
5. How can Newton’s third law be observed in these situations?

Tip: Always ensure the net force direction is consistent when summing forces acting on an object.