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

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.

You are watching: Acceleration due to gravity in meters per second squared

Note!

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)

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:


Time (s)VelocityDistancem/skm/hft/smphmft
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! 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.

*

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

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:

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

Sponsored Links

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

*

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro.Add the Engineering ToolBox extension to your SketchUp from the SketchUp Pro Sketchup Extension Warehouse!


Privacy

We don"t collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don"t save this data.

Google use cookies for serving our ads and handling visitor statistics. Please read Google Privacy & Terms for more information about how you can control adserving and the information collected.

AddThis use cookies for handling links to social media. Please read AddThis Privacy for more information.


Advertise in the ToolBox

If you want to promote your products or services in the Engineering ToolBox - please use Google Adwords. You can target the Engineering ToolBox by using AdWords Managed Placements.


Citation

This page can be cited as

Engineering ToolBox, (2003). Acceleration of Gravity and Newton"s Second Law. Available at: https://www.smashville247.net/accelaration-gravity-d_340.html .

See more: Does Olive Oil Help Stretch Marks ? Can Olive Oil Help With Stretch Marks

Modify access date.