High School

A see-saw is 800 cm long and is supported at its center. A boy weighing 40 kgf sits 1 m from the end of the see-saw on one side. Where should a man weighing 60000 gf sit to balance the see-saw?

Answer :

To solve this problem, we need to use the concept of moments and equilibrium from physics.

A see-saw balances when the moments (or turning forces) on either side of the fulcrum (the pivot point at the center) are equal.

The formula for the moment is:

[tex]\text{Moment} = \text{Force} \times \text{Distance from the fulcrum}[/tex]

Let's break down the problem step by step:

  1. Identify Given Values:

    • The see-saw is 800 cm long; therefore, it is supported at its center, so each side is 400 cm or 4 m long.
    • The boy sits 1 m from the end of the see-saw, which means he is [tex]4 - 1 = 3[/tex] m from the fulcrum.
    • The boy weighs 40 kgf.
    • The man weighs 60000 gf, which can be converted to 60 kgf (since 1000 gf = 1 kgf).

  2. Calculate the Moment for the Boy:

    • Moment due to the boy [tex]= 40 \text{ kgf} \times 3 \text{ m} = 120 \text{ kgf\cdot m}[/tex].

  3. Set Up the Equation for the Man's Position:

    • Let [tex]x[/tex] be the distance the man should sit from the fulcrum to balance the see-saw.
    • The moment due to the man [tex]= 60 \text{ kgf} \times x \text{ m}[/tex].

  4. Equation for Balance:

    • For the see-saw to be in equilibrium (balanced), the moments must be equal:

      [tex]60 \times x = 120[/tex]

    • Solving for [tex]x[/tex]:

      [tex]x = \frac{120}{60} = 2 \text{ m}[/tex]

  5. Conclusion:

    • The man should sit 2 meters from the fulcrum to balance the see-saw.

By placing the man 2 meters from the center on the see-saw, the turning forces on either side are balanced, achieving equilibrium.

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