is it true that when a piece of paper and a stone are dropped from height,they fall at the same time and why?

Answer 1

Depends. In air, the answer is obviously No. But in a vacuum, such as on the surface of the moon, the answer would be Yes. Air resistance is much more effective at slowing the speed of something large and lightweight.

Answer 2

This is true if and only if there are no other forces other than gravity acting on the two bodies. If there is drag friction, for example, the paper will clearly fall slower...like a falling leaf.

If the only force at work is weight = W = mg; so that, g = W/m = constant for a given distance (R) from the center of mass M causing the gravitation force (like the center of Earth).

Thus, even if the stone weight W = 100 X w the weight of the paper we'd have W = Mg = 100 w and w = mg; so that W/w = Mg/mg = 100w/w = 100. Thus, Mg = 100 mg and M = 100 m. In other words, when something weighs more, like the stone, its mass is also more. And that keeps g = weight/mass at the same value no matter how much something weighs.

Answer 3

Yes, it is true (provided they are in vacuum i.e. no air resistance that I believe you imply). Why? Because the acceleration (which is in both cases g = 9.81 m/s^2) are the same. And since acceleration is the second derivative (in time) of the path it means that both pieces will have the same path length for the same time. Now inverse, for the same path length, both bodies will spend the same time. Translated, it means that both bodies dropped from the same height will fall at the same time. (As a kid, I have tried it to drop big stone and small stone from the bridge. They reach the water at the same time.)

Answer 4

They fall at the same velocity *ONLY* if they fall in a vacuum. The equation to determine the rate an object would fall is g = G*m / r^2 :: 'g' is rate of acceleration, 'G' is the gravitational constant, 'm' is the mass of the attracting mass, and 'r' is its radius. Notice that there's nothing in the equation about the mass of the object being dropped (..accelerated..)

Long ago, one of our Apollo astronauts did an experiment on the moon. He dropped a feather and a hammer from the same height and they both reached the surface at the same time.

Answer 5

Under normal conditions they don't, the paper receives a considerable amount of air resistance so the stone falls fist. In vacuum they do, this is because the acceleration of a falling object its independent of the object's mass. In F=ma, where F (force) represents gravity, the accelerations is contact. A difference in mass affects the force of the earth on the object, and not the acceleration. There is a complex math proof of that, but unfortunately I cannot show it here. Please refer to Newtons law of gravitation in respect to the earth and small masses on it.

Answer 6

You can practice this yourself. In vacuum, two objects dropped from the same height will hit the ground at the same time. This is because the ACCELERATION of gravity is nearly constant on Earth. This applies to all objects, despite their mass. Now the FORCE that gravity exerts on these objects is different. Objects with greater mass have a greater gravitational force exerted on them:

F = mg
F: force due to gravity
m: mass of object
g: acceleration of gravity.

But g is always constant, on all objects. Objects will always fall at the same rate (if they're dropped on the same planet).

Answer 7

Equivalence Principle: All local objects vacuum free fall identically - along parallel minimum action trajectories - regardless of chemical composition or mass distribution.

Google
"nordtvedt effect" 816 hits

It is unknown whether chemically identical opposite chirality mass distributions - a left and a right shoe - violate the Equivalence Principle. General Relativity and string theory demand they fall identically. Einstein-Cartan; affine, teleparallel, and non-commutative gravitation theories allow them to diverge by at least 10^(-13) difference/average.

http://www.mazepath.com/uncleal/lajos.htm#a2
experiment
http://www.mazepath.com/uncleal/qz4.pdf
background and different experiment

Answer 8

they start falling at the same time but do not land at the same time this is because the paper has a low terminal velocity.

Answer 9

do you mean at the same rate? if so yes, but only in a perfect vaccum (no matter at all in the area) otherwise it depends on the aerodynamics of the object and its mass.

Answer 10

move on to the next question peter, if your stuck!.......would a pound (coin) fall at the same speed as an ounce ( mountain lion)?