Rotational Motion and Law of Gravity

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SUMMARY

The discussion focuses on solving problems related to gravitational force and torque in rotational motion. The gravitational force between two objects is given as 9.30 x 10-9 N, with a total mass of 5.06 kg. Participants utilized Newton's law of gravitation, F = Gm1m2/r2, to derive the individual masses, confirming that m1 + m2 = 5.06 kg. Additionally, the torque calculation related to a dental bracket exerting a force of 86.2 N was discussed, although specific solutions were not provided.

PREREQUISITES
  • Understanding of Newton's law of gravitation
  • Basic algebra for solving equations
  • Knowledge of torque and its calculation
  • Familiarity with force components in physics
NEXT STEPS
  • Study the derivation of gravitational force equations in detail
  • Learn how to calculate torque using the formula τ = r × F
  • Explore the concept of force components and their applications in physics
  • Practice solving problems involving gravitational force and mass calculations
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Students studying physics, educators teaching gravitational concepts, and anyone interested in understanding rotational motion and torque calculations.

madeeeeee
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a) Two objects attract each other with a gravitational force of magnitude 9.30 x10-9 N when separated by 19.4 cm. If the total mass of the objects is 5.06 kg, what is the mass of each?

Heavier mass_______kg
Lighter mass______ kg

my attempt:
F=Gm1m2/r^2
so I rearranged to get m1 and m2 by itself and got (r^2)(F)/G=m1m2
5.247598=m1m2
but how do I get the mass for m1 and m2 separately is m1 + m2 = 5.06 kg?


b) A dental bracket exerts a horizontal force of 86.2 N on a tooth at point B in the figure. What is the torque on the root of the tooth about point A? (PLEASE SEE THE ATTACHMENT FOR THE PICTURE)

I know I need to break the forces up into components but I am lost on this question. Please help me! Thank you
 

Attachments

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madeeeeee said:
a) Two objects attract each other with a gravitational force of magnitude 9.30 x10-9 N when separated by 19.4 cm. If the total mass of the objects is 5.06 kg, what is the mass of each?

Heavier mass_______kg
Lighter mass______ kg

my attempt:
F=Gm1m2/r^2
so I rearranged to get m1 and m2 by itself and got (r^2)(F)/G=m1m2
5.247598=m1m2
but how do I get the mass for m1 and m2 separately is m1 + m2 = 5.06 kg?

Yes, the total mass is given as 5.06 kg, so m1 + m2 = 5.06 kg. Replace one of the masses, say m2, with m2 = (5.06 kg - m1).
 
I used this and found my answer to be .433 and 4.627 but its wrong. Do i have my formula correct?
 
madeeeeee said:
I used this and found my answer to be .433 and 4.627 but its wrong. Do i have my formula correct?

Your formula (Newton's law of gravitation) looks okay. Perhaps something went wrong in your math manipulations. If you post your calculations they can be checked.
 
actually I just solved it! It was just a silly error! But thank you for your help

Do you have nay idea how to do part b ?
 
madeeeeee said:
actually I just solved it! It was just a silly error! But thank you for your help

Do you have nay idea how to do part b ?

What are your thoughts? What do you think you need to know in order to proceed?
 

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