m = mass (kg, slugs )
a g = g = acceleration of gravity (9.81 m/s 2 , 32.17405 ft/s 2 )
The force caused by gravity - a g - is called weight .
The acceleration of gravity can be observed by measuring the change of velocity related to change of time for a free falling object:
a g = dv / dt (2)
dv = change in velocity (m/s, ft/s)
dt = change in time (s)
An object dropped in free air accelerates to speed 9.81 m/s (32.174 ft/s) in one - 1 - second .
1 a g = 1 g = 9.81 m/s 2 = 35.30394 (km/h)/s
1 a g = 1 g = 32.174 ft/s 2 = 386.1 in/s 2 = 22 mph/s
The velocity for a free falling object after some time can be calculated as:
v = a g t (3)
v = velocity (m/s)
The distance traveled by a free falling object after some time can be expressed as:
s = 1/2 a g t 2 (4)
s = distance traveled by the object (m)
The velocity and distance traveled by a free falling object:
Note! Velocities and distances are achieved without aerodynamic resistance ( vacuum conditions). The air resistance - or drag force - for objects at higher velocities can be significant - depending on shape and surface area.
A stone is dropped from 1470 ft (448 m) - approximately the height of Empire State Building. The time it takes to reach the ground (without air resistance) can be calculated by rearranging (4) :
t = (2 s / a g ) 1/2
= (2 (1470 ft) / (32.174 ft/s 2 )) 1/2
= 9.6 s
The velocity of the stone when it hits the ground can be calculated with (3) :
v = (32.174 ft/s 2 ) (9.6 s)
= 308 ft/s
= 210 mph
= 94 m/s
= 338 km/h
A ball is thrown straight up with an initial velocity of 25 m/s . The time before the ball stops and start falling down can be calculated by modifying (3) to
t = v / a g
= (25 m/s) / (9.81 m/s 2 )
= 2.55 s
The distance traveled by the ball before it turns and start falling down can be calculated by using (4) as
s = 1/2 (9.81 m/s 2 ) ( 2.55 s ) 2
= 31.8 m
"Every body continues in a state of rest or in a uniform motion in a straight line, until it is compelled by a force to change its state of rest or motion."
"To every action there is always an equal reaction - if a force acts to change the state of motion of a body, the body offers a resistance equal and directly opposite to the force."
Acceleration of gravity varies with latitude - examples:
|Location||Latitude||Acceleration og Gravity |
(m/s 2 )
|North Pole||90° 0'||9.8321|
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