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Let's work through this problem step-by-step:

### Problem 4-33:
A 60-inch television, with a mass of 3.11 slugs, is loaded onto a truck using a ramp as shown in the diagram. We are tasked with determining the forces acting on the TV and the angle of inclination of the ramp.

#### Part (a) - Determine the angle \(\theta\):
We are given:
- Height of the ramp \( h = 3 \, \text{ft} \)
- Base of the ramp \( b = 10 \, \text{ft} \)

Using basic trigonometry, the angle \(\theta\) can be calculated using the tangent function:
\[
\tan(\theta) = \frac{h}{b}
\]
Let's calculate the angle \(\theta\).

#### Part (b) - Friction force \( \vec{F} \), Normal force \( \vec{N} \), and Weight \( \vec{W} \):
The forces acting on the TV in the free-body diagram include:
- **Weight \( \vec{W} \)**: Given by \( W = mg \), where \( m = 3.11 \, \text{slugs} \) and \( g = 32.2 \, \text{ft/s}^2 \). The weight will be calculated in pounds-force (lbf).
- **Normal force \( \vec{N} \)**: Acts perpendicular to the ramp.
- **Friction force \( \vec{F} \)**: Acts parallel to the ramp, opposing motion.

We'll write these forces in terms of unit vectors (\(\hat{i}, \hat{j}\)).

#### Part (c) - Solving the equilibrium equation:
Finally, we substitute the forces into the equilibrium equation:
\[
\vec{F} + \vec{N} + \vec{W} = 0
\]
This will allow us to determine the values of \( F \) and \( N \) in pounds-force (lbf).

Let me first calculate part (a) and the weight from part (b).For Part (a), the angle of the ramp \(\theta\) is approximately **16.7°**.

For Part (b), the weight \(W\) of the television is approximately **100.14 lbf**.

Next, we'll write the friction force \( \vec{F} \), normal force \( \vec{N} \), and weight \( \vec{W} \) in rectangular form and solve for \( F \) and \( N \) in the equilibrium equation. Shall I proceed with these steps?

A 60-inch television, with a mass of 3.11 slugs, is loaded onto a truck using a ramp. Given h = 3 ft and b = 10 ft, determine the angle θ. Calculate the friction force, normal force, and weight of the TV, and solve for equilibrium using F + N + W = 0.

Solve a statics problem involving a 60-inch TV with a mass of 3.11 slugs loaded onto a truck using a ramp. Learn how to calculate the angle of inclination, friction force, normal force, and weight. Use equilibrium equations to determine unknown forces.

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