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# galileo law of falling bodies

From Wikipedia

Free fall

right|thumb|Scott conducting an experiment during the [[Apollo 15]] moon landing.

Free fall is any motion of a body where gravity is the only or dominant force acting upon it, at least initially. These conditions produce an inertial trajectory so long as gravity remains the only force. Since this definition does not specify velocity, it also applies to objects initially moving upward. Since free fall in the absence of forces other than gravity produces weightlessness or "zero-g," sometimes any condition of weightlessness due to inertial motion is referred to as free-fall. This may also apply to weightlessness produced because the body is far from a gravitating body.

Although strict technical application of the definition excludes motion of an object subjected to other forces such as aerodynamic drag, in nontechnical usage, falling through an atmosphere without a deployed parachute, or lifting device, is also often referred to as free fall. The drag forces in such situations prevent them from producing full weightlessness, and thus a skydiver's "free fall" after reachingterminal velocity produces the sensation of the body's weight being supported on a cushion of air.

## Examples

thumb|A video showing objects free-falling 215 feet (65 m) down a metal well, a type of drop tube Examples of objects in free fall include:

• A spacecraft (in space) with propulsion off (e.g. in a continuous orbit, or on a suborbital trajectory going up for some minutes, and then down).
• An object dropped at the top of a drop tube.
• An object thrown upwards or a person jumping off the ground at low speed (i.e. as long as air resistance is negligible in comparison to weight). Technically, the object or person is in free fall even when moving upwards or instantaneously at rest at the top of their motion, since the acceleration is still g downwards. However in common usage "free fall" is understood to mean downwards motion.

Since all objects fall at the same rate in the absence of other forces, objects and people will experience weightlessness in these situations.

Examples of objects not in free fall:

• Flying in an aircraft: there is also an additional force of lift.
• Standing on the ground: the gravitational acceleration is counteracted by the normal force from the ground.
• Descending to the Earth using a parachute, which balances the force of gravity with an aerodynamic drag force (and with some parachutes, an additional lift force).

The example of a falling skydiver who has not yet deployed a parachute is not considered free fall from a physics perspective, since they experience a drag force which equals their weight once they have achieved terminal velocity (see below). However, the term "free fall skydiving" is commonly used to describe this case in everyday speech, and in the skydiving community. It is not clear, though, whether the more recent sport of wingsuit flying fits under the definition of free fall skydiving.

### On Earth and on the Moon

Near the surface of the Earth, an object in free fall in a vacuum will accelerate at approximately 9.8&nbsp;m/s^{2}, independent of its mass. With air resistance acting upon an object that has been dropped, the object will eventually reach a terminal velocity, around 56&nbsp;m/s (200&nbsp;km/h or 120&nbsp;mph) for a human body. Terminal velocity depends on many factors including mass, drag coefficient, and relative surface area, and will only be achieved if the fall is from sufficient altitude.

Free fall was demonstrated on the moon by astronaut David Scott on August 2, 1971. He simultaneously released a hammer and a feather from the same height above the moon's surface. The hammer and the feather both fell at the same rate and hit the ground at the same time. This demonstrated Galileo's discovery that in the absence of air resistance, all objects experience the same acceleration due to gravity. (On the Moon, the gravitational acceleration is much less than on Earth, approximately 1.6&nbsp;m/s^{2}).

## Free fall in Newtonian mechanics

### Uniform gravitational field without air resistance

This is the "textbook" case of the vertical motion of an object falling a small distance close to the surface of a planet. It is a good approximation in air as long as the force of gravity on the object is much greater than the force of air resistance, or equivalently the object's velocity is always much less than the terminal velocity (see below).

v(t)=-gt+v_{0}\,
y(t)=-\frac{1}{2}gt^2+v_{0}t+y_0

where

v_{0}\, is the initial velocity (m/s).
v(t)\,is the vertical velocity with respect to time (m/s).
y_0\, is the initial altitude (m).
y(t)\, is the altitude with respect to time (m).
t\, is time elapsed (s).
g\, is the acceleration due to gravity (9.81 m/s2 near the surface of the earth).

### Uniform gravitational field with air resistance

This case, which applies to skydivers, parachutists or any bodies with Reynolds number well above the critical Reynolds number, has an equation of motion:

m\frac{dv}{dt}=\frac{1}{2} \rho C_{\mathrm{D}} A v^2 - mg \, ,

where

m is the mass of the object,
g is the gravitational acceleration (assumed constant),
CD is the drag coefficient,
A is the cross-sectional area of the object, perpendicular to air flow,
v is the fall (vertical) velocity, and
Ï� is the air density.

Assuming an object falling from rest and no change in air density with altitude, the solution is:

v(t) = -v_{\infty} \tanh\left(\frac{gt}{v_\infty}\right),

where the terminal speed is given by

v_{\infty}=\sqrt{\frac{2mg}{\rho C_D A}} \, .

The object's velocity versus time can be integrated over time to find the vertical position as a function of time:

y = y_0 - \frac{v_{\infty}^2}{g} \ln \cosh\left(\frac{gt}{v_\infty}\right).

When the air density cannot be assumed to be constant, such as for objects or skydivers falling f

Question:...our group represents Galileo for the debate..pls help us..we need to defend the law of Galileo against the law of Aristotle..hope you can help us..thanks :D if you know something about it..pls tell us your reasons and ideas :D

Answers:Galileo proved his law of motion (Things in free fall fall at the same rate regardless of mass) by experiment. (Dropping objects off the Tower of Pisa and rolling different mass balls down ramps) There is no debate that he is correct. It has been tested and proven. Aristotle reached his conclusion by "reason" without testing it. He thought about it and concluded that more massive objects would fall faster. Made sense to him so it must be true. No need to test. (EDIT:This is demonstrably false. Both Newton and Galileo proved that this is not the case. Scientific Proof rests on: We live in a rational consistent universe. ====> Do the same thing the same way and you will get the same result. Even Quantum Mechanics that is probabilistic has rules that cannot be violated. You cannot know the position and momentum of a particle at the same time. The better you know one the worse you know the other. It is not uncommon for engineers to accept the reality of phenomena that are not yet understood, as it is very common for physicists to disbelieve the reality of phenomena that seem to contradict contemporary beliefs of physics - H. Bauer It is fun being an engineer, we are the least rigorous of the math and science community. That opens up whole new worlds of things that are possible. True story from my Grad School days: My professor of Numerical Analysis was doing a proof used for Finite Element models. At one step a math major stopped him with, " Professor, you cannot do that! You cannot prove it is true for all cases." The professor stopped, thought for a minute, and said, "You're right. Never the less it is true." Then he continued with the proof. The answer to, "You cannot prove that!" Is, "Yes, but how much are you willing to bet I am wrong? I'll even give you odds."

Question:

Answers:Civil law. It might fall under a sub-set of real property restrictions or housing ordinances, or zoning regulations, etc..., but it is under the civil body of law.

Question:Determined to test the law of gravity himself, a student walks off a skyscraper 180 m high, stopwatch in hand, and starts his free fall(0 initial velocity). Five sec. later, Superman arrives at the scene and dives off the roof to save the student. a.) Superman leaves the roof with an initial speed v0 that he produces by pushing himself downward from the edge of the roof with his legs of steel. He then falls with the same acceleration as any freely falling body. What must the value of v0 be so that Superman catches the student just before they reach the ground? b.)if the height of the skyscraper is less than some minimum value, even Superman can t reach the student before he hits the ground. What is this minimum height?

Answers:Working formula is S = Vo(T) + (1/2)gT^2 where S = distance travelled Vo = initial velocity T = time interval g = acceleration due to gravity = 9.8 m/sec^2 For the student, S = 0 + (1/2)(9.8)(T^2) S = 4.9T^2 For Superman, S = Vo(T - 5) + (1/2)(9.8)(T - 5)^2 For Superman to catch the student, 4.9T^2 = Vo(T - 5) + (1/2)(9.8)(T - 5)^2 4.9T^2 = Vo(T - 5) + 4.9(T^2 - 10T + 25) 4.9T^2 = Vo(T - 5) + 4.9T^2 - 49T + 122.5 Solving for Vo, Vo = (49T - 122.5)/(T - 5) -- call this Equation 3 Going back to Equation 1, since "Superman catches the student just before they reach the ground?" , then 180 = 4.9(T^2) and solving for "T" T = 6.06 sec. Substituting T = 6.06 into Equation 3, Vo = (49*6.06 - 122.5)/(6.06 - 5) Vo = 168 m/sec. << if the height of the skyscraper is less than some minimum value, even Superman can t reach the student before he hits the ground. What is this minimum height? >> The calculated values for the above were based on the given data of the problem. ASSUMING all the conditions remain the same, then if the height of the skyscraper were less than 180 m, then Superman cannot save the student before he hits the ground. Hope this helps.

Question:It is not a motion with a constant acceleration as the earth gravitation is changing inversely with the square of distance between two corps according with Newton's gravitation law.

Answers:If you begin with Newtons laws of motion and gravity, it would be very difficult for you to figure out how to integrate equations of motion. Beter write potential energy in form PE = GMm/R and use conservation of energy. Better yet use the following approach: The falling body obeys the three laws of Kepler. Write the laws and try to figure out how time depends on altitude t=t(h). No calculus required. It is easier to figure out what will happen if the body has small initial horizontal velocity, the body falling strictly vertically would be the limiting case. Time dependence on altitude t(h) can be expressed in elemetary functions, but not altitude depedence on time h(t).