A question about Newton's Law of Universal Gravitation

AI Thread Summary
The discussion revolves around calculating the mass of a smaller sphere using Newton's Law of Universal Gravitation, given a gravitational force and the mass of a larger sphere. The initial calculations yielded an incorrect mass due to unit conversion errors from centimeters to meters. After correcting the distance to 1.05 meters, the revised mass calculated was 50.4 kg, which still seemed too large. Participants noted that "smaller" could refer to size rather than mass, but the calculations have consistently focused on mass. The conversation emphasizes the importance of unit consistency in gravitational calculations.
Spongemonkies
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Homework Statement


The gravitational force between two shperes is 2.50x10^-8. Their centers are 105 cm apart. The larger sphere has a mass of 8.20 kg. Find the mass of the smaller sphere.


Homework Equations


F=Gm1m2/d²


The Attempt at a Solution


F=Gm1m2/d²
d² x F=Gm1m2/d² x d²
Fd²=Gm1m2
Fd²/Gm1=Gm1m2/Gm1
Fd²/Gm1=m2

m2=((2.50x10^-8 N)(105² cm))/((6.67x10^-11 Nm²/kg²)(8.20 kg))
m2=5.04x10^5 kg

That can't be right because the missing mass is supposed to be smaller than 8.20 kg. Did I move the equation around right?
 
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Are you mixing the units cm and m inappropriately?

- Warren
 
Okay, I forgot to convert cm to m.

But using d=1.05 meters, I get 50.4 kg as my answer. It's closer, but still too large. :frown:
 
Spongemonkies said:
Okay, I forgot to convert cm to m.

But using d=1.05 meters, I get 50.4 kg as my answer. It's closer, but still too large. :frown:

I agree with your result.

By "smaller" sphere they may have meant smaller in size, not necessarily smaller in mass.
 
So far though, we've only used mass for those problems.
 
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