Acceleration of Gravity and Newton's Second Law
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Acceleration of Gravity and Newton's Second LawAcceleration of gravity and Newton's Second Law - SI and Imperial units
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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."
Newton's second law for the gravity force - weight - can be expressed as
F = m g (1)
where
F = force, weight (N, lbf)
m = mass (kg, slugs)
g = acceleration of gravity (9.81 m/s2, 32.17405 ft/s2)
The force caused by gravity - g - is called weight. Note! Mass - m - is a property.
The acceleration of gravity can be observed by measuring the change of velocity of a free falling object:
g = dv / dt (2)
where
dv = change in velocity (m/s, ft/s)
dt = change in time (s)
A dropped object accelerate to a speed of 9.81 m/s or 32.174 ft/s in one second.
heavy and light bodies near the earth falls toward the earth with the same acceleration
Acceleration of Gravity in SI Units
1 g = 9.81 m/s2 = 35.30394 (km/h)/s
Acceleration of Gravity in Imperial Units
1 g = 32.174 ft/s2 = 386.1 in/s2 = 22 mph/s
Velocity and Distance Traveled of a Free Falling ObjectThe velocity of a free fall object can be expressed as:
v = g t (3)
where
v = velocity
The distance traveled by a free falling object can be expressed as:
s = 1/2 g t2 (4)
where
s = distance traveled by the object
The velocity and distance traveled by a free falling object:
Time (s)
Velocity Distance
m/s km/h ft/s mph m ft
1 9.8 35.3 32.2 21.9 4.9 16.1
2 19.6 70.6 64.3 43.8 19.6 64.3
3 29.4 106 96.5 65.8 44.1 144.8
4 39.2 141 128.7 87.7 78.5 257.4
5 49.1 177 160.9 110 122.6 402.2
6 58.9 212 193.0 132 176.6 579.1
7 68.7 247 225.2 154 240.3 788.3
8 78.5 283 257.4 176 313.9 1,029.6
9 88.3 318 289.6 198 397.3 1,303.0
10 98.1 353 321.7 219 490.5 1,608.7
Note! The velocities are achieved without aerodynamical resistance (vacuum). The air resistance is significant for higher velocities or for objects withlarger surface area to mass ratio - like feathers or similar.
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 airresistance) can be calculated by rearranging eq. (4):
t = (2 s / g)1/2
= (2 (1470 ft) / (32.174 ft/s2 ))1/2
= 9.6 s
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 UpA ball is thrown straight up with an initial velocity of 25 m/s. The time before the ball stops and start falling can be calculated by modifying (3) to
t = v / g
= (25 m/s) / (9.81 m/s2)
= 2.55 s
The distance traveled by the ball before it turns 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 ormotion."
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 anddirectly opposite to the force."
Common Expressions
superimposed loads: kN/m2
mass loads: kg/m2 or kg/m3 stress: N/mm2
bending moment: kNmshear: kN
1 N/mm = 1 kN/m
1 N/mm2 = 103 kN/m2
1 kNm = 106 Nmm
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Related Topics
Basics - Basic Information as SI-system, Unit converters, Physical constantsDynamics - Dynamics Motion - velocity and acceleration
Mechanics - Kinematics, forces, vectors, motion, momentum, energy and the dynamics of objects
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Tag Search
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