Acceleration of Gravity and Newton's Second Law
Acceleration 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)
m = mass
g = acceleration of gravity
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
dt = change in time
A dropped object accelerate to a speed of 9.81 m/s or 32.174 ft/s in one second.
Acceleration of Gravity in SI Units
g = 9.81 m/s2
Acceleration of Gravity in Imperial Units
g = 32.174 ft/s2
Velocity and Distance Traveled of a Free Falling Object
The velocity of a free falling 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 velocity is achieved without any aero-dynamical resistance (vacuum). The air resistance will be significant for higher velocities or for object with large surface area to mass ratio - feathers or similar.
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."
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