To calculate the gravitational force and the normal force, we will break it down step by step:

Gravitational Force:

The gravitational force acting on the block is given by: $F_{\text{gravity}} = m \cdot g$ where:

• $m = 3.5 \, \text{kg}$ (mass of the block),
• $g = 9.8 \, \text{m/s}^2$ (acceleration due to gravity).

$F_{\text{gravity}} = 3.5 \cdot 9.8 = 34.3 \, \text{N}.$

Normal Force:

If the block is pushed along a horizontal floor with no vertical component of force, the normal force ($F_{\text{normal}}$) balances the gravitational force. Hence: $F_{\text{normal}} = F_{\text{gravity}} = 34.3 \, \text{N}.$

However, if the pushing force $F = 15 \, \text{N}$ had a vertical component, this would affect $F_{\text{normal}}$. Assuming no such vertical component, the normal force equals the gravitational force.

Final Answer:

• Gravitational Force: $34.3 \, \text{N}$ downward.
• Normal Force: $34.3 \, \text{N}$ upward.

Let me know if you'd like further clarification or details.

---

Related Questions:

1. What happens to the normal force if the force $F$ has an upward or downward vertical component?
2. How would the normal force change if the surface was inclined instead of horizontal?
3. What additional forces would act on the block if there was friction?
4. How would the motion of the block be analyzed using Newton's Second Law?
5. What happens to the normal force if the gravitational acceleration $g$ changes?

Tip:

Always draw a free-body diagram for force-related problems to visualize and identify all acting forces