As shown, a pipe is anchored to a wall at point A. (Figure 2)      During the pipe's installation, several forces are applied to the pipe at different locations. If  F1
= 17.7  lb
,  F2
= 16.5  lb
,  F3
= 12.6  lb
,  F4
= 10.1  lb
,  d1
= 0.400  ft
,  d2
= 0.750  ft
, and  d3
= 0.650  ft
, what is  MRA
, the net moment about point A due to these forces? Assume that moments acting counterclockwise about point A are positive whereas moments acting clockwise are negative.
Express your answer numerically in pound-feet to three significant figures.

To determine the net moment \( M_{RA} \) about point A, we need to calculate the moments produced by each of the forces \( F_1 \), \( F_2 \), \( F_3 \), and \( F_4 \) with respect to point A. The moment produced by a force is given by the equation:

\[
M = F \times d
\]

Where:
- \( F \) is the magnitude of the force,
- \( d \) is the perpendicular distance from point A to the line of action of the force,
- The direction of the moment (clockwise or counterclockwise) will determine the sign (positive or negative).

### Forces and Distances:
- \( F_1 = 17.7 \, \text{lb} \) at \( d_1 = 0.400 \, \text{ft} \)
- \( F_2 = 16.5 \, \text{lb} \) at \( d_2 = 0.750 \, \text{ft} \)
- \( F_3 = 12.6 \, \text{lb} \) at \( d_3 = 0.650 \, \text{ft} \)
- \( F_4 = 10.1 \, \text{lb} \), no distance specified (assumed to act directly at point A, which would contribute zero moment).

### Moment Calculation:
- For \( F_1 \) at \( d_1 \), assume it generates a counterclockwise moment (positive):
  \[
  M_1 = 17.7 \, \text{lb} \times 0.400 \, \text{ft} = 7.08 \, \text{lb-ft}
  \]

- For \( F_2 \) at \( d_2 \), assume it generates a clockwise moment (negative):
  \[
  M_2 = -16.5 \, \text{lb} \times 0.750 \, \text{ft} = -12.375 \, \text{lb-ft}
  \]

- For \( F_3 \) at \( d_3 \), assume it generates a counterclockwise moment (positive):
  \[
  M_3 = 12.6 \, \text{lb} \times 0.650 \, \text{ft} = 8.19 \, \text{lb-ft}
  \]

- For \( F_4 \), since no distance is provided, we assume the moment is zero:
  \[
  M_4 = 0
  \]

### Net Moment:
The net moment about point A is the sum of the individual moments:
\[
M_{RA} = M_1 + M_2 + M_3 + M_4
\]
\[
M_{RA} = 7.08 + (-12.375) + 8.19 + 0 = 2.895 \, \text{lb-ft}
\]

Thus, the net moment about point A is:

\[
M_{RA} = 2.90 \, \text{lb-ft}
\]

### Final Answer:
The net moment about point A is \( \boxed{2.90 \, \text{lb-ft}} \).

---

Do you want details or have any questions? Here are some follow-up questions you might explore:

1. What are the conditions under which a moment is considered positive or negative?
2. How would the net moment change if the forces were applied at different angles instead of perpendicular distances?
3. What would happen if \( F_4 \) had a specified distance from point A?
4. How do the units of force and distance affect the calculation of moments?
5. How can the principle of moments be applied in real-world engineering scenarios?

**Tip:** When summing moments, always make sure to pay attention to the direction (clockwise or counterclockwise) to ensure the correct sign is applied.

As shown, a pipe is anchored to a wall at point A. (Figure 2) During the pipe's installation, several forces are applied to the pipe at different locations. If F1 = 17.7 lb, F2 = 16.5 lb, F3 = 12.6 lb, F4 = 10.1 lb, d1 = 0.400 ft, d2 = 0.750 ft, and d3 = 0.650 ft, what is MRA, the net moment about point A due to these forces? Assume that moments acting counterclockwise about point A are positive whereas moments acting clockwise are negative. Express your answer numerically in pound-feet to three significant figures.

Learn how to calculate the net moment about point A during pipe installation with forces of F1 = 17.7 lb, F2 = 16.5 lb, F3 = 12.6 lb, and F4 = 10.1 lb applied at various distances. This problem involves the use of statics principles, moment calculations, and equilibrium conditions, suitable for college-level engineering students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation