Understanding Forces Applied in the Same Direction

Statement I is correct. When multiple forces are applied to an object and they all act in the same direction, the total effect is the sum of the individual forces. This means the forces add up to create a larger resultant force.

For example, if two people push a box, and both push towards the east:

• Person A pushes with a force of $F_A = 10$ Newtons (N) east.
• Person B pushes with a force of $F_B = 5$ Newtons (N) east.

The net force ($F_{\text{net}}$) acting on the box is the sum of these forces:

$$F_{\text{net}} = F_A + F_B$$

$$F_{\text{net}} = 10 \text{ N} + 5 \text{ N} = 15 \text{ N}$$

The net force is 15 N east. This confirms that forces in the same direction add to one another.

Analyzing Forces Acting in Opposite Directions

Statement II is also correct. When two forces act on an object in opposite directions, they counteract each other. The net force acting on the object is the difference between the magnitudes of the two forces. The direction of the net force is the same as the direction of the stronger force.

Consider the same box, but now the forces are applied in opposite directions:

• Person A pushes with a force of $F_A = 10$ Newtons (N) east.
• Person B pushes with a force of $F_B = 5$ Newtons (N) west.

To find the net force, we subtract the smaller force from the larger force. Let's assign east as the positive direction:

$$F_{\text{net}} = F_A + (-F_B)$$

$$F_{\text{net}} = 10 \text{ N} + (-5 \text{ N})$$

$$F_{\text{net}} = 10 \text{ N} - 5 \text{ N} = 5 \text{ N}$$

Since the result is positive, the net force is 5 N towards the east, which is the direction of the larger applied force. This confirms that the net force is the difference between the two opposing forces.

Conclusion on Force Statements

Both statement I and statement II accurately describe how forces combine when applied to an object. Therefore, both statements are correct.