If a car and golf ball fall from the same height in a vaccum do they reach the ground at the same time?

Question

If yes, why if the other has much more mass

Answer 1

The acceleration due to gravity is constant for all objects regardless of mass. We can understand this as follows:

The force due to gravity is given as

F = G*(m_obj*m_earth)/r²; where G is the universal gravitation constant

Now also, F = m_obj*a

Equating these we have

m_obj * a = G*(m_obj * m_earth)/r²

OR

a = G*m_earth/r²

I.e. the acceleration is independent of the object's mass.

Answer 2

Yes, it is true that, without air resistance, mass has very little to do with the acceleration due to gravity of an object. This can actually be demonstated with the theory of conservation of energy, where you can show mathematically that mass completely cancels out when finding the speed at which something falls:

Let's take an object with mass "m" that is dropped from a height of "h" with no initial velocity, and we will denote the prime symbol ( ' ) as the final state.

"Initial Energy" = "Final Energy"
==> two forms of energy, potential and kinetic
[ P.E. + K.E. ] = [ P.E. + K.E. ]'
==> now, there is no initial kinetic energy b/c it is dropped from rest, and no final potential energy b/c it ends up on the ground
[ P.E. + 0 ] = [ 0 + K.E. ]'
==> let's plug in the equations
mgh = ½mv²
==> mass CANCELS on both sides
gh = ½mv²
==> multiply by 2 on each side
2gh = v²
==> square root both sides
v = √(2gh)

As you can see, the final velocity of any object only depends upon the height from which it was dropped and the constant acceleration due to gravity. Therefore, any two objects with different masses will fall at the same rate, as long as air resistance is neglected.

Answer 3

Yes.. they will both reach the ground at the same time. Counter-intuitive.. i know.. but the physics is such ( assuming acceleration due to gravity as 10 m/s ^2)

then displacement s = 5 t^2 ....

since s is constant then it follows that t has to be the same for both objects...

One thing to note is that the time to reach ground is independent of the mass of the object.

Answer 4

They do hit the ground at the same time.

The gravitational force on the car (a.k.a. its "weight") is certainly greater than the gravitational force on the golf ball. And it is true that greater force tends to increase an object's acceleration.

But the car also has a greater _mass_; and greater mass tends to _decrease_ an object's acceleration (i.e., it makes it "harder" to change the object's speed).

These two effects exactly cancel each other out. The earth pulls harder on the car, but the car resists the pull more; so it ends up falling exactly as fast as the golf ball.

Answer 5

Yes. During the Apollo 15 mission astronaut David Scott dropped a hammer and a feather on the moon and they fell at the same rate.

Answer 6

Matter falls at the same rate in a vacuum regardless of mass.

Answer 7

Yes as per Galileo

Answer 8

Yes.

Mass has little to do with the rate of acceleration due to gravity.