Center of gravity of a stack of coins

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SUMMARY

The center of gravity of a stack of coins consisting of five nickels and four pennies is calculated using the formula Y center of gravity = (y1m1 + y2m2 + ... + ynmn) / (m1 + m2 + ... + mn). The correct calculation reveals that the center of gravity is approximately 1.80 mm above the tabletop, which is inconsistent with the total height of the stack, roughly 15 mm. The error arises from not considering the individual positions of each coin in the stack, leading to an incorrect assumption that all coins share the same center of mass.

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KatlynEdwards
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Homework Statement



A penny has a mass of 2.5 g and is 1.5 mm thick; a nickel has a mass of 5.7 g and is 1.9 mm thick.

If you make a stack of coins on a table, starting with five nickels and finishing with four pennies, how far above the tabletop is the center of gravity of the stack?

Homework Equations



Y center of gravity = (y1m1+y2m2+y3m3 etc) / (m1+m2+m3 etc)

The Attempt at a Solution



Ycg = (5*(5.7*1.9)+4*(2.5*1.5)) / ((5*5.7) +(4*2.5))
Ycg = 1.80 mm

This answer doesn't make sense because the entire stack is roughly 15 mm high... What am I doing wrong?
 
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KatlynEdwards said:

Homework Statement



A penny has a mass of 2.5 g and is 1.5 mm thick; a nickel has a mass of 5.7 g and is 1.9 mm thick.

If you make a stack of coins on a table, starting with five nickels and finishing with four pennies, how far above the tabletop is the center of gravity of the stack?

Homework Equations



Y center of gravity = (y1m1+y2m2+y3m3 etc) / (m1+m2+m3 etc)

The Attempt at a Solution



Ycg = (5*(5.7*1.9)+4*(2.5*1.5)) / ((5*5.7) +(4*2.5))
Ycg = 1.80 mm

This answer doesn't make sense because the entire stack is roughly 15 mm high... What am I doing wrong?
I'm just looking at this quickly so hopefully I'm not missing something, but the equation says Y_cg = (y1m1 + y2m2+...)/(m1+m2+...), those y's are coordinates. So the way you've done it, each coin has its centre of mass at the same place (so all the nickels are at (0, 1.9) and all the pennies are at (0, 1.5). Draw it out, so you can see the positions in the stack.
 
Yep that was it :D Awesome! Thanks for the help.
 

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