In a vacuum, why doesn’t an elephant accelerate faster than a penny as it falls to the ground?

Answer 1

Newton recognized that any two masses, not matter what they are, experience a force of attraction. His universal law of gravitation is F = (Gm₁m₂)/r² where G is a constant 6.67×10‾¹¹ [(Nm²)/kg²], m₁ and m₂are any two masses in kg, and r is the separation of the masses in meters measured from each center of mass.

When you (or any mass) are close to earth and m₁ is you and m₂ is the earth, the distance between your center of masses is the radius of the earth. If you substitute the radius of the earth for r and the mass of the earth for m₂, the universal law of gravitation equation becomes F = m₁(9.8meters/s²) = m₁g where g is the gravitational acceleration g = 9.8m/s² and is independent of mass m₁. It does not matter which mass is m₁ or m₂. All objects near earth's surface in a vacuum fall with the same gravitational acceleration of 9.8m/s².

If you don't have a vacuum, then you will have air drag opposing motion, which increases with speed and varies with the shape of the object. Similarly shaped objects with different masses should experience similar drag forces and fall at the same rate. Brian Cox has a nice youtube video that shows a bowling ball vs feather drop in air and in a vacuum which is worth a look. Enjoy and good luck! https://www.youtube.com/watch?v=E43-CfukEgs&t=6s

Answer 2

It all comes down to Newton's 2nd Law which states Fnet=ma

If we have an elephant we obviously have a big mass but also a big force.

If we rewrite the equation above we get acc=Big Force/Big Mass for the elephant and Tiny Force/Tint mass for a penny. The ratio will always be the same.

So in a vacuum both will accelerate at 9.8 m/s^2t\

^{If there is air resistance the terminal velocity will depend upon mass and shape. The elephant would definitely be traveling faster than the penny when it hits the ground.}

Answer 3

Newton recognized that any two masses, not matter what they are, experience a force of attraction. His universal law of gravitation is F = (Gm₁m₂)/r² where G is a constant 6.67×10‾¹¹ [(Nm²)/kg²], m₁ and m₂ are any two masses in kg, and r is the separation of the masses in meters measured from each center of mass.

When you (or any mass) are close to earth and m₁ is you and m₂ is the earth, the distance between your center of masses is the radius of the earth. If you substitute the radius of the earth for r and the mass of the earth for m₂, the universal law of gravitation equation becomes F = m₁(9.8meters/s²) = m₁g where g is the gravitational acceleration g = 9.8m/s² and is independent of mass m₁. It does not matter which mass is m₁ or m₂. All objects near earth's surface in a vacuum fall with the same gravitational acceleration of 9.8m/s².

If you don't have a vacuum, then you will have air drag opposing motion, which increases with speed and varies with the shape of the object. Similarly shaped objects with different masses should experience similar drag forces and fall at the same rate. Brian Cox has a nice youtube video that shows a bowling ball vs feather drop in air and in a vacuum which is worth a look. Enjoy and good luck! https://www.youtube.com/watch?v=E43-CfukEgs&t=6s