A meter stick of uniform material has some dough stuck on one end. The stick has a mass of 0.1 kg. It will balance when supported at a point 0.33m from the dough. How much mass does the dough have?

Answers

Answer 1

At the equilibrium or balance point the meter stick stationary and the sum of the moments and forces acting on it is zero

The mass of the dough is .[tex]\underline {51.\overline{51}}[/tex] grams

Reason:

Known;

Length of the stick = 1 meter

Mass of the stick, m = 0.1 kg

Point the stick will balance when the dough is at one end = 0.33 m

Required:

How much mass does the dough have

Solution:

The meter stick is balanced when the clockwise moment and the anticlockwise moment about the balance point are equal

Let M, represent the mass of the dough, we have;

The center of mass of the meter stick = The 0.5 m point

Taking moment, we have;

[tex]\mathbf{\sum M_{clockwise} = \sum M_{anticlockwise}}[/tex]

Distance from the center of mas of the ruler to the fulcrum, d₁ = (0.5 - 0.33) m

Distance from the dough to the fulcrum, d₂ = 0.33 m

Clockwise moment, [tex]\mathbf{\sum M_{clockwise} }[/tex] = m × d₁

Anticlockwise moment, [tex]\mathbf{\sum M_{anticlockwise} }[/tex] = M × d₂

Therefore;

(0.5 - 0.33) × 0.1 = M × 0.33

Therefore, we get;

[tex]M = \dfrac{(0.5 - 0.33) \times 0.1}{0.33} =\dfrac{17}{330} =0. 0\overline{51}[/tex]

The mass the dough has, M = 0.0[tex]\overline{51}[/tex] kg = 51.[tex]\underline{\overline{51}}[/tex] grams

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