Question

i) will a sheet of papper fall slower than one that is crumpled into a ball in vaccum? why?
ii) show mathametically that acceleration experiment by an object is independent of its mass.
iii)show that the value of g =9.8 m/s square

Answer 1

1)no because there is no air resistance in vaccum... all objects fall at the same rate in the absence of air
2) consider a body of mass 'm' on the surface of the earth .. its distance from the centre of the earth is 'R'(radius of the earth).
the gravitational force experienced by the body is F= GMm/R^2 , where M is the mass of the earth
From Newton's second law of motion ,
F= mg
Equating the above two forces ,
GMm/R^2 = mg
therefore,
g=GM/R^2

This equation shows that 'g' is independent of mass of the body 'm' but it varies with the distance from the centre of the earth..If earth is assumed to be an sphere of radius R, the value of g on the surface of earth is a constant

Answer 2

Answer:

No, Alec is incorrect

Explanation:

For objects on the surface (or close to the surface) of the earth, gravitational accelerationwill always remain the same, regardless of shape.

Think about some of the kinematic equations we'd use to model a falling object under the influence of gravity:

Δ(y)=v0yt−12gt2
2(−g)Δy=v2f−v20

Do you see a mass in any of these equations? No! These equations are independent of mass, because gravitational acceleration is solely dependent on the mass of the earth. The reasons for this are not too difficult to understand (I daresay you'll study them very soon), but in the interests of not straying too much, I will just link you to this video by Khan Academy that explains it, which you can watch if interested.

Why does the crumpled paper fall faster though? Well, that's because there is also air resistance acting on these two objects. A flatter piece of paper invites more air to push against it, while the crumpled sheet is does not.

All this says, however, is that they fall at different speeds due to the different magnitudes of air resistance acting on them. Not due to "lesser" gravitational acceleration.

If you were to repeat this experiment in vacuum, you'd discover that both fall at the same time. In fact, you could drop an elephant and a feather and they'd hit the ground at the same time! That's pretty cool, and goes to prove our point that acceleration due to gravity does not depend on the masses of the objects in question, and certainly not on whether or not they're crumpled.

Hope that helped :)