Center of gravity of a stack of coins

In summary, the conversation discusses the calculation of the center of gravity of a stack of coins on a table, given the masses and thicknesses of pennies and nickels. The equation used is Y_cg = (y1m1 + y2m2+...)/(m1+m2+...), where y represents the coordinates and m represents the masses of the coins. However, the initial attempt at solving the problem did not take into account the varying positions of the coins in the stack, resulting in an inaccurate answer. A visual representation of the stack can help in understanding the correct method of calculation.
  • #1
KatlynEdwards
28
0

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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  • #2
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.
 
  • #3
Yep that was it :D Awesome! Thanks for the help.
 

1. What is the center of gravity of a stack of coins?

The center of gravity of a stack of coins is the point at which the weight of the stack is evenly distributed in all directions. It is also known as the center of mass.

2. How is the center of gravity of a stack of coins determined?

The center of gravity of a stack of coins can be determined by balancing the stack on a pivot point and marking the point where it is perfectly balanced. This point is the center of gravity.

3. Does the number of coins in a stack affect its center of gravity?

Yes, the number of coins in a stack does affect its center of gravity. As more coins are added to the stack, the center of gravity shifts towards the bottom of the stack.

4. Can the shape of the coins in a stack affect its center of gravity?

Yes, the shape of the coins in a stack can affect its center of gravity. For example, if the coins are stacked in a pyramid shape, the center of gravity will be higher compared to a stack of coins that are stacked in a straight line.

5. How does the center of gravity of a stack of coins affect its stability?

The center of gravity of a stack of coins plays a crucial role in its stability. If the center of gravity is too high, the stack is more likely to topple over. A lower center of gravity provides more stability and makes the stack less likely to fall over.

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