How can Newtonian gravity be converted to m/s without prefix?

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SUMMARY

The discussion focuses on converting gravitational force, represented by the equation Fgrav=(GMm)/(r^2), into acceleration units of m/s² rather than velocity units of m/s. It clarifies that gravitational force is measured in Newtons and can be converted to acceleration using Newton's Second Law, F=ma. The acceleration due to gravity can be expressed as a_{gravity}=\frac{GM}{r^2}, where M is the mass of the object creating the gravitational field.

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  • Familiarity with gravitational force equations (Fgrav=(GMm)/(r^2))
  • Knowledge of unit conversion between force and acceleration
  • Basic concepts of mass and gravitational fields
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TheNormalForc
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Before I inundate you with various elementary problems I'm facing, I need help with the concept.

Fgrav=(GMm)/(r^2)

So Fgrav is in units of Newtons, correct? How would one convert that to m/s?
 
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Gravity is just a force an object with mass experiences, which can be translated to acceleration with Newton's 2nd Law, F=ma. It has nothing to do with velocity (which has units m/s). However you can turn it into units of m/s^2, which is the units of acceleration with the above mentioned law: a=F/m, therefore:
[tex] a_{gravity}=\frac{GM}{r^2}[/tex]

Where M is the mass of the object that is creating the gravitational field, not the "accelerating object".
 
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