Gravity Hammer

Lore & Background

In the Western world prior to the 16th century, it was generally assumed that the speed of a falling body would be proportional to its weight—that is, a 10 kg object was expected to fall ten times faster than an otherwise identical 1 kg object through the same medium. The ancient Greek philosopher Aristotle (384–322 BC) discussed falling objects in Physics (Book VII), one of the oldest books on mechanics. Although, in the 6th century, John Philoponus challenged this argument and said that, by observation, two balls of very different weights will fall at nearly the same speed. In 12th-century Iraq, Abu'l-Barakāt al-Baghdādī gave an explanation for the gravitational acceleration of falling bodies. According to Shlomo Pines, al-Baghdādī's theory of motion was "the oldest negation of Aristotle's fundamental dynamic law [namely, that a constant force produces a uniform motion], [and is thus an] anticipation in a vague fashion of the fundamental law of classical mechanics [namely, that a force applied continuously produces acceleration]." In 1551 Domingo de Soto became the first to state that a body in free fall accelerates uniformly and that this acceleration is caused by the mass of the Earth. This key concept of physics was essential for the later studies of gravity by Galileo and Newton. Galileo credited De Soto as his inspiration and source of his studies, but Isaac Newton, despite having read Galileo Galilei, never mentioned him. In the 20th century, Pierre Duhem credited him with important achievements in dynamics and viewed his work as a forerunner of modern mechanics. According to a tale that may be apocryphal, in 1589–1592 Galileo dropped two objects of unequal mass from the Leaning Tower of Pisa. Given the speed at which such a fall would occur, it is doubtful that Galileo could have extracted much information from this experiment. Most of his observations of falling bodies were really of bodies rolling down ramps. This slowed things down enough to the point where he was able to measure the time intervals with water clocks and his own pulse (stopwatches having not yet been invented). He repeated this "a full hundred times" until he had achieved "an accuracy such that the deviation between two observations never exceeded one-tenth of a pulse beat." In 1589–1592, Galileo wrote De Motu Antiquiora, an unpublished manuscript on the motion of falling bodies.

In Their Own Story

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 (ballistics) going up for some minutes, and then down). An object dropped at the top of a drop tube. An object thrown upward or a person jumping off the ground at low speed (i.e. as long as air resistance is negligible in comparison to weight). Technically, an object is in free fall even when moving upwards or instantaneously at rest at the top of its motion. If gravity is the only influence acting, then the acceleration is always downward and has the same magnitude for all bodies, commonly denoted g. 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 force 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 that equals their weight once they have achieved terminal velocity. Near the surface of the Earth, an object in free fall in a vacuum will accelerate at approximately 9.8 m/s2, independent of its mass. With air resistance acting on an object that has been dropped, the object will eventually reach a terminal velocity, which is around 53 m/s (190 km/h or 118 mph) for a human skydiver. The 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. A typical skydiver in a spread-eagle position will reach terminal velocity after about 12 seconds, during which time they will have fallen around 450 m (1,500 ft). 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 surface 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, however, the gravitational acceleration is approximately 1.63 m/s2, or only about 1/6 that on Earth.

Reader's Guide

In Newtonian mechanics, for a 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. The equations are: v(t) = v0 - gt and y(t) = v0 t + y0 - (1/2) g t^2, where v0 is the initial vertical component of the velocity (m/s), v(t) is the vertical component of the velocity at t (m/s), y0 is the initial altitude (m), y(t) is the altitude at t (m), t is time elapsed (s), and g is the acceleration due to gravity (9.81 m/s2 near the surface of the earth). If the initial velocity is zero, then the distance fallen from the initial position will grow as the square of the elapsed time: v(t) = -gt and y0 - y(t) = (1/2) g t^2. Moreover, because the odd numbers sum to the perfect squares, the distance fallen in successive time intervals grows as the odd numbers. This description of the behavior of falling bodies was given by Galileo. For a uniform gravitational field with air resistance, this case applies to skydivers, parachutists or any body of mass, m, and cross-sectional area.

Did You Know?

• In the 6th century, John Philoponus challenged Aristotle's argument about falling objects and said that, by observation, two balls of very different weights will fall at nearly the same speed.
• In 1551 Domingo de Soto became the first to state that a body in free fall accelerates uniformly and that this acceleration is caused by the mass of the Earth.
• Free fall was demonstrated on the Moon by astronaut David Scott on August 2, 1971, when he simultaneously released a hammer and a feather from the same height above the Moon's surface, and they both hit the surface at the same time.
• A typical skydiver in a spread-eagle position will reach terminal velocity after about 12 seconds, during which time they will have fallen around 450 m (1,500 ft).
• Near the surface of the Earth, an object in free fall in a vacuum will accelerate at approximately 9.8 m/s2, independent of its mass.