Let's break down and solve the questions based on the image you uploaded.

Part (a):

Weight of the box (m₁ = 17.5 kg): The weight $W$ is calculated using the formula: $W = m \cdot g$ Where:

• $m$ is the mass of the object (17.5 kg),
• $g$ is the acceleration due to gravity, which is approximately $9.8 \, \text{m/s}^2$.

So, the weight of the box: $W = 17.5 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 171.5 \, \text{N}$

The normal force acting on the box is equal to the weight of the box when it's at rest on a flat surface. So the normal force is also: $N = 171.5 \, \text{N} \, \text{(upward)}$

Part (b):

When a 13.0 kg box (m₂) is placed on top of the 17.5 kg box:

1. Normal force that the table exerts on the 17.5 kg box (combined weight of both boxes): The combined mass of the two boxes is: $m_{\text{total}} = 17.5 \, \text{kg} + 13.0 \, \text{kg} = 30.5 \, \text{kg}$ The total weight is: $W_{\text{total}} = 30.5 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 298.9 \, \text{N}$ So, the normal force that the table exerts on the 17.5 kg box is: $N_{\text{table}} = 298.9 \, \text{N}$

2. Normal force that the 17.5 kg box exerts on the 13.0 kg box: The normal force exerted by the 17.5 kg box on the 13.0 kg box is equal to the weight of the 13.0 kg box: $N_{\text{box}} = 13.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 127.4 \, \text{N}$

Summary of Answers:

1. Weight of the 17.5 kg box = 171.5 N.
2. Normal force acting on the 17.5 kg box = 171.5 N (upward).
3. Normal force the table exerts on the 17.5 kg box (with 13.0 kg box on top) = 298.9 N (upward).
4. Normal force the 17.5 kg box exerts on the 13.0 kg box = 127.4 N (upward).

Would you like any further details or have any questions?

Here are 5 related questions to deepen understanding:

1. What happens to the normal force if the surface is inclined instead of flat?
2. How does the normal force change if the boxes are accelerating upward or downward?
3. How would friction affect the forces if the table was not frictionless?
4. What is the significance of the direction of the normal force in these calculations?
5. How would these calculations change on a planet with a different gravity, like Mars?

Tip: The normal force is always perpendicular to the surface on which the object rests.