---
title: "A non-uniform horizontal plank of mass \\(M\\) and length \\(L\\) has its center of mass located at a distance \\(\\dfrac{L}{3}\\) from its left end. The plank rests horizontally on two vertical sawhorses: Sawhorse 1 at \\(x = 0\\) and Sawhorse 2 at \\(x = L\\). A point load of mass \\(M\\) is placed on the plank at position \\(x\\).  | | \\(F_{N,1}\\) (Load at \\(x = \\dfrac{2}{3}L\\)) | \\(F_{N,2}\\) (Load at \\(x = \\dfrac{2}{3}L\\)) | \\(F_{N,1}\\) (Load at \\(x = L\\)) | |—|—|—|—| | Row A | \\(\\dfrac{5}{6}Mg\\) | \\(\\dfrac{7}{6}Mg\\) | \\(\\dfrac{1}{2}Mg\\) | | Row B | \\(\\dfrac{4}{3}Mg\\) | \\(\\dfrac{2}{3}Mg\\) | \\(\\dfrac{5}{3}Mg\\) | | Row C | \\(Mg\\) | \\(Mg\\) | \\(\\dfrac{2}{3}Mg\\) | | Row D | \\(\\dfrac{1}{3}Mg\\) | \\(\\dfrac{2}{3}Mg\\) | \\(0\\) |  Which row in the table correctly identifies the upward normal forces \\(F_{N,1}\\) and \\(F_{N,2}\\) exerted by the sawhorses for the given load positions?"
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date_modified: "2026-08-23T04:43:49+00:00"
---

# A non-uniform horizontal plank of mass \(M\) and length \(L\) has its center of mass located at a distance \(\dfrac{L}{3}\) from its left end. The plank rests horizontally on two vertical sawhorses: Sawhorse 1 at \(x = 0\) and Sawhorse 2 at \(x = L\). A point load of mass \(M\) is placed on the plank at position \(x\).

| | \(F_{N,1}\) (Load at \(x = \dfrac{2}{3}L\)) | \(F_{N,2}\) (Load at \(x = \dfrac{2}{3}L\)) | \(F_{N,1}\) (Load at \(x = L\)) |
|—|—|—|—|
| Row A | \(\dfrac{5}{6}Mg\) | \(\dfrac{7}{6}Mg\) | \(\dfrac{1}{2}Mg\) |
| Row B | \(\dfrac{4}{3}Mg\) | \(\dfrac{2}{3}Mg\) | \(\dfrac{5}{3}Mg\) |
| Row C | \(Mg\) | \(Mg\) | \(\dfrac{2}{3}Mg\) |
| Row D | \(\dfrac{1}{3}Mg\) | \(\dfrac{2}{3}Mg\) | \(0\) |

Which row in the table correctly identifies the upward normal forces \(F_{N,1}\) and \(F_{N,2}\) exerted by the sawhorses for the given load positions?

A non-uniform horizontal plank of mass \(M\) and length \(L\) has its center of mass located at a distance \(\dfrac{L}{3}\) from its left end. The plank rests horizontally on two vertical sawhorses: Sawhorse 1 at \(x = 0\) and Sawhorse 2 at \(x = L\). A point load of mass \(M\) is placed on the plank at position \(x\).

| | \(F_{N,1}\) (Load at \(x = \dfrac{2}{3}L\)) | \(F_{N,2}\) (Load at \(x = \dfrac{2}{3}L\)) | \(F_{N,1}\) (Load at \(x = L\)) |
|---|---|---|---|
| Row A | \(\dfrac{5}{6}Mg\) | \(\dfrac{7}{6}Mg\) | \(\dfrac{1}{2}Mg\) |
| Row B | \(\dfrac{4}{3}Mg\) | \(\dfrac{2}{3}Mg\) | \(\dfrac{5}{3}Mg\) |
| Row C | \(Mg\) | \(Mg\) | \(\dfrac{2}{3}Mg\) |
| Row D | \(\dfrac{1}{3}Mg\) | \(\dfrac{2}{3}Mg\) | \(0\) |

Which row in the table correctly identifies the upward normal forces \(F_{N,1}\) and \(F_{N,2}\) exerted by the sawhorses for the given load positions?

![A horizontal bar representing a plank of length \(L\) is supported at its bottom left corner by a triangular support labeled Sawhorse 1 at \(x = 0\) and at its bottom right corner by a triangular support labeled Sawhorse 2 at \(x = L\). A filled circle on the plank marks the center of mass of the plank at a horizontal position \(\dfrac{L}{3}\) from the left end. A square block labeled \(M\) sits on top of the plank. A horizontal coordinate line below the setup indicates \(x = 0\) directly beneath Sawhorse 1 and \(x = L\) directly beneath Sawhorse 2. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460229-4NFYvv.jpg)

- **A.** Row A
- **B.** Row B
- **C.** Row C
- **D.** Row D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120865/*