Simple object falling to earth question

[wallz]

Can anybody help me with this question...
according to classical mechanics what determines the magnitude of the acceleration of an object falling to Earth ignoring air resistance?

i'm not sure if this is a trick question but isn't it just gravity and the mass of the object?

 

[rock.freak667]

From Newton's law of Gravitation and Newton's 2nd Law

F = ma = GMm/r^2

or a = GM/r^2

so the acceleration does not depend on the mass of the object.

In essence it depends on gravity, but you can extend it to other parameters.

 

[wallz]

Thank you! this was my first post and i do have other questions, can i just ask them on this thread?

 

[gneill]

Write Newton's equation for f, the force of gravity by the Earth on a body of mass m (let M be the mass of the Earth). By Newton's second law, f = ma. So find the acceleration, a, of the body. What does it depend upon?

 

[wallz]

so basically it depends on gravity? and how high it is off the surface of the earth?

 

[gneill]

rock.freak667 provided a formula.

a = GM/r^2

What constants and what variables do you see in there? What do each of them represent?

 

[abejackson]

I was wondering if we could apply W=F(ma) times D to this problem.
Because of gravity an object would have an uniform acceleration and the mass of the object will remain constant. But an increase or a decrease of the distance would determine the total amount of work done. I think it's a trick question because the question asks what would determine the magnitude of the acceleration but we know that the acceleration will be the same. Please correct me if I'm wrong about something.

 

[gneill]

The magnitude of the acceleration due to gravity is only approximately constant over a small change in radial distance from the center of the Earth. a = GM/r². We use a standard value for g that is a representative value over much of the Earth's surface.

If a falling body's change in radial distance not a negligible fraction of the radius (Δr/r is not very small), then one cannot consider the acceleration due to gravity to be constant over the trajectory.