Acceleration of Gravity and Newtons Second Law

Acceleration of gravity and Newtons Second Law - SI and Imperial units.

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Acceleration of gravity is one of the most used physical constants - most 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 velocity of a free falling object:

g = dv / dt (2)

where

dv = change in velocity

dt = change in time

If we drop an object we will observe that it will 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 ft/s m ft
1 9.8 32.2 4.9 16.1
2 19.6 64.3 19.6 64.3
3 29.4 96.5 44.1 144.8
4 39.2 128.7 78.5 257.4
5 49.1 160.9 122.6 402.2
6 58.9 193.0 176.6 579.1
7 68.7 225.2 240.3 788.3
8 78.5 257.4 313.9 1,029.6
9 88.3 289.6 397.3 1,303.0
10 98.1 321.7 490.5 1,608.7

Note! The velocity is achieved without any aero-dynamical resistance (vacuum). Obviously the air resistance will be significant for increasing velocities.

Newton's First Law

"Every body continues in a state of rest or in 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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Related Topics

  • Basics Basic Information as SI-system, Unit converters, Physical constants...
  • Mechanics Kinematics, forces, vectors, motion, momentum, energy and the dynamics of objects

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