Acceleration of Gravity and Newton's Second Law

Acceleration of gravity and Newton's Second Law - SI and Imperial units

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

g = 9.81 m/s2

Acceleration of Gravity in Imperial Units

g = 32.174 ft/s2 = 386.1 in/s2 = 35 kph/s = 22 mph/s

Velocity and Distance Traveled of a Free Falling Object

The 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 with larger surface area to mass ratio - like feathers or similar.

distance velocity free falling object

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 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 Up

A 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 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

Related Topics

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

Related Documents

Key Words

  • en: acceleration gravity newton's second law
  • es: segunda ley de Newton aceleraciĆ³n de la gravedad
  • de: Beschleunigung der Schwerkraft Newtons zweites Gesetz

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