Calculate force on the diagram below if the beam is balanced. Write data aside.

Question

ScanSolve AI Tutor · Accepted Answer

Here's how to calculate the unknown force P using the principle of moments:

Identify the known values from the diagram.
The force on the left side is $F_L = 60 \, \text{N}$ .
The distance from the fulcrum to the left force is $d_L = 0.2 \, \text{m}$ .
The distance from the fulcrum to the unknown force P is $d_R = 0.1 \, \text{m}$ .
The beam is balanced, meaning the sum of clockwise moments equals the sum of anti-clockwise moments.
Apply the principle of moments.
The anti-clockwise moment is produced by the $60 \, \text{N}$ force.
The clockwise moment is produced by the force P.
For a balanced beam:
$\text{Anti-clockwise moment} = \text{Clockwise moment}$ $F_L \times d_L = P \times d_R$
Substitute the values into the equation and solve for P.
$60 \, \text{N} \times 0.2 \, \text{m} = P \times 0.1 \, \text{m}$ $12 \, \text{N}\cdot\text{m} = P \times 0.1 \, \text{m}$ $P = \frac{12 \, \text{N}\cdot\text{m}}{0.1 \, \text{m}}$ $P = 120 \, \text{N}$
The unknown force P is $120 \, \text{N}$ .

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