Taking [tex]g = 10 \; \text{N}\cdot \text{kg}^{-1}[/tex].
- Worker A: 476 N.
- Worker B: 324 N.
Explanation
Worker A:
Consider the pipe as a level. Worker A will supply the effort, and worker B will act as the fulcrum.
- Worker A applies an upward force 4.2 meters away from the fulcrum.
- The weight of the pipe acts at the center of its mass, which is 2.5 meters away from the fulcrum. The level is class two.
[tex]4.2 \times F_\text{A} = 2.5 \times m\cdot g\\[/tex]
[tex]F_\text{A} = \dfrac{2.5}{4.2} \; m\cdot g\\\phantom{F_\text{A}} = \dfrac{2.5}{4.2} \times 80 \times 10\\\phantom{F_\text{A}} = 476 \; \text{N}[/tex]
Worker B:
Again, consider the pipe as a level. Worker B will now supply the effort, and worker A will act as the fulcrum.
- Worker B applied an upward force [tex]F_\text{B}[/tex] 4.2 meters away on the left-hand side of the fulcrum.
The weight of the pipe acts at two positions.
- [tex]\dfrac{4.2}{5.0}[/tex] of the pipe's mass acts downwards between worker A and B. That [tex]\dfrac{4.2}{5.0} \times 80 \; \text{kg}[/tex] of mass will act downward at its center of mass [tex]\dfrac{1}{2} \times 4.2\;\text{m}[/tex] away on the left-hand side of the fulcrum. [tex]F_\text{1} = \dfrac{4.2}{5.0} \times 80 \times 10 = 672 \; \text{N}[/tex]
- [tex]\dfrac{0.8}{5.0}[/tex] of the pipe's mass acts downwards to the right of worker B. That [tex]\dfrac{0.8}{5.0} \times 80 = 12.8 \; \text{kg}[/tex] of mass will act also downward at its center of mass [tex]\dfrac{1}{2} \times 0.8\;\text{m}[/tex] away on the right-hand side of the fulcrum. [tex]F_\text{2} = \dfrac{0.8}{5.0} \times 80 \times 10 = 128 \; \text{N}[/tex]
[tex]\underbrace{F_\text{B} \cdot l_\text{B} - F_{1} \cdot l_{1}}_{\text{Left-Hand Side}} =\underbrace{-F_{2} \cdot l_{2}}_{\text{Right-Hand Side}}[/tex] for the pipe to balance. Therefore:
[tex]F_\text{B} = \dfrac{F_{1} \cdot l_{1} - F_{2} \cdot l_{2}}{l_\text{B}} \; \\\phantom{F_\text{B}} = \dfrac{672 \times \dfrac{4.2}{2} - 128 \times \dfrac{0.8}{2}}{4.2} \\\phantom{F_\text{B}} = 324\; \text{N}[/tex].
Make sure that [tex]F_\text{A} + F_\text{B}= m \cdot g = 800 \; \text{N}[/tex].
