How Much Sand Is Needed to Balance a Plank Horizontally?

AI Thread Summary
To balance the 2.00-m, 25.0-kg plank horizontally on a fulcrum at its midpoint, the mass of sand needed in the box must be calculated using the center of gravity equation. The center of gravity of the plank is located 50.0 cm from the right end, which affects the distribution of mass. The equation x_cg = (m_p(0) + m_s(0.25)) / (25 + m_s) is set up to find the required mass of sand (m_s). The position of the fulcrum is crucial, as it determines the balance point. The goal is to ensure the combined center of gravity of the system is at the fulcrum's position for equilibrium.
iwonde
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Homework Statement


A box of negligible mass rests at the left end of a 2.00-m, 25.0-kg plank (see image). The width of the box is 75.0 cm, and sand is to be distributed uniformly throughout it. The center of gravity of the nonuniform plank is 50.0 cm from the right end. What mass of sand should be put into the box so that the plank balances horizontally on a fulcrum placed just below its midpoint?

centerofgravity.jpg


Homework Equations


x_cg = (sum of (the masses x position)) / sum of the masses


The Attempt at a Solution


m_p = mass of plank
m_s = mass of sand
x_cg= (m_p(0)+m_s(0.25))/(25+m_s)
I don't know what to set the equation of x-cg equal to. Please help.
 
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It's equal to whatever position you called the fulcrum
 

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