Acceleration of Gravity is one of the most used physical constants – known from
Newton’s Second Law
“Change of motion is proportional to the force applied, and take place along the straight line the force acts.”
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Newton’s second law for the gravity force – weight – can be expressed as
W = Fg
= m ag
= m g (1)
where
W, Fg = weight, gravity force (N, lbf)
m = mass (kg, slugs)
ag = g = acceleration of gravity (9.81 m/s2, 32.17405 ft/s2)
The force caused by gravity – ag – is called weight.
Note!
- mass is a property – a quantity with magnitude
- force is a vector – a quantity with magnitude and direction
The acceleration of gravity can be observed by measuring the change of velocity related to change of time for a free falling object:
ag = dv / dt (2)
where
dv = change in velocity (m/s, ft/s)
dt = change in time (s)
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An object dropped in free air accelerates to speed 9.81 m/s (32.174 ft/s) in one – 1 – second.
- a heavy and a light body near the earth will fall to the earth with the same acceleration (when neglecting the air resistance)
Acceleration of Gravity in SI Units
1 ag = 1 g = 9.81 m/s2 = 35.30394 (km/h)/s
Acceleration of Gravity in Imperial Units
1 ag = 1 g = 32.174 ft/s2 = 386.1 in/s2 = 22 mph/s
Velocity and Distance Traveled by a Free Falling Object
The velocity for a free falling object after some time can be calculated as:
v = ag t (3)
where
v = velocity (m/s)
The distance traveled by a free falling object after some time can be expressed as:
s = 1/2 ag t2 (4)
where
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.
- Acceleration of gravity on the North and South Pole – and on Equator
Example – Free Falling Stone
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 / ag)1/2
= (2 (1470 ft) / (32.174 ft/s2 ))1/2
= 9.6 s
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The velocity of the stone when it hits the ground can be calculated with (3):
v = (32.174 ft/s2) (9.6 s)
= 308 ft/s
= 210 mph
= 94 m/s
= 338 km/h
Example – A Ball Thrown Straight Up
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 / ag
= (25 m/s) / (9.81 m/s2)
= 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/s2) (2.55 s)2
= 31.8 m
Newton’s First Law
“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.”
Newton’s Third Law
“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.”
Common Expressions
- superimposed loads: kN/m2
- mass loads: kg/m2 or kg/m3
- stress: N/mm2
- bending moment: kNm
- shear: kN
- 1 N/mm = 1 kN/m
- 1 N/mm2 = 103 kN/m2
- 1 kNm = 106 Nmm
Latitude and Acceleration of Gravity
Acceleration of gravity varies with latitude – examples:
Acceleration of Gravity vs. Location and Latitude LocationLatitudeAcceleration og Gravity(m/s2) North Pole 90° 0′ 9.8321 Anchorage 61° 10′ 9.8218 Greenwich 51° 29′ 9.8119 Paris 48° 50′ 9.8094 Washington 38° 53′ 9.8011 Panama 8° 55′ 9.7822 Equator 0° 0′ 9.7799
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