To calculate the gravitational and normal forces acting on the block, let's analyze the problem step by step:

1. Gravitational Force ($F_g$):

The gravitational force is simply the weight of the block, calculated as:

$F_g = m \cdot g$

Where:

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

$F_g = 3.5 \cdot 9.8 = 34.3 \, \text{N}$

So, the gravitational force is:

$F_g = 34.3 \, \text{N}$

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2. Normal Force ($F_N$):

The normal force is affected by the vertical components of the applied force and the gravitational force. The applied force ($F$) at an angle of $40^\circ$ has a vertical component $F \sin \theta$, which reduces the normal force acting on the block.

The normal force is given by:

$F_N = F_g - F \sin \theta$

Where:

• $F = 15 \, \text{N}$ (magnitude of the applied force)
• $\theta = 40^\circ$

First, calculate the vertical component of the applied force:

$F \sin \theta = 15 \cdot \sin(40^\circ)$

Using $\sin(40^\circ) \approx 0.6428$:

$F \sin \theta = 15 \cdot 0.6428 = 9.64 \, \text{N}$

Now, subtract this from the gravitational force to find the normal force:

$F_N = 34.3 - 9.64 = 24.66 \, \text{N}$

So, the normal force is approximately:

$F_N = 24.7 \, \text{N}$

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Final Results:

1. Gravitational Force: $F_g = 34.3 \, \text{N}$
2. Normal Force: $F_N = 24.7 \, \text{N}$

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Would you like detailed step-by-step diagrams or explanations?

Expanding Questions:

1. How does the angle of the applied force affect the normal force?
2. What happens to the normal force if the angle increases to $60^\circ$?
3. If friction is added, how do we calculate the net force on the block?
4. What is the significance of the horizontal component of the applied force in this scenario?
5. How would the results change if the block's mass were doubled?

Tip:

Always resolve forces into components when dealing with inclined or angled forces to simplify calculations.