**Unit of Weight:**

Unit of Weight – the force at which earth or any other gravity generating astral body attracts objects, it’s a vector value. In common use weight is often confused with mass.

**Weight:**

Weight is the gravitational force acting on a body mass. The generic expression of Newton’s Second Law (1) can be transformed to express weight as a force by replacing the acceleration – a – with the acceleration of gravity – g – as

W = m g (2)

where

W = weight or gravitational force – F (N, lb_{f})

m = mass (kg, slugs)

g = acceleration of gravity on earth (9.81 m/s^{2}, 32.17405 ft/s^{2})

The British Gravitational System (Imperial System) of units is used by engineers in the English-speaking world with the same relation to the foot – pound – second system as the meter – kilogram – force second system (SI) has to the meter – kilogram – second system. For engineers who deals with forces, instead of masses, it’s convenient to use a system that has as its base units length, time, and force, instead of length, time and mass.

The three base units in the Imperial system are the foot, the second, and the pound-force.

In the BG system the mass unit is the slug and is defined from the Newton’s Second Law (1). The unit of mass, the slug, is derived from the pound-force by defining it as the mass that will accelerate at 1 foot per second per second when a 1 pound-force acts upon it:

1 lb = (1 slug)(1 ft/s^{2})

In other words, 1 lb (pound) force acting on 1 slug mass will give the mass an acceleration of 1 ft/s^{2}.

The weight of the mass from equation (2) in BG units can be expressed as:

w (lb) = m (slugs) g (ft/s^{2})

With standard gravity – g = 32.17405 ft/s^{2} – the mass of 1 slug weights 32.17405 lb_{f }(pound-force).

The English Engineering System – EE

In the English Engineering system of units the primary dimensions are are force, mass, length, time and temperature. The units for force and mass are defined independently

- the basic unit of mass is pound-mass (lb
_{m}) - the unit of force is the pound (lb) alternatively pound-force (lb
_{f}).

In the EE system 1 lb of force will give a mass of 1 lb_{m} a standard acceleration of 32.17405 ft/s^{2}.

Since the EE system operates with these units of force and mass, the Newton’s Second Law can be modified to

F = m a / g_{c} (3)

where

g_{c} = a proportionality constant

or transformed to weight

w = m g / g_{c} (4)

The proportionality constant g_{c} makes it possible to define suitable units for force and mass. We can transform (4) to

1 lb_{f} = (1 lb_{m}) (32.174 ft/s^{2}) / g_{c}

or

g_{c} = (1 lb_{m}) (32.174 ft/s^{2}) / (1 lb_{f})

Since 1 lb_{f} gives a mass of 1 lb_{m} an acceleration of 32.17405 ft/s^{2} and a mass of 1 slug an acceleration of 1 ft/s^{2}, then

1 slug = 32.17405 lb_{m.}

Useful for CBSE, ICSE, NCERT & International Students

Grade :9

Subject : Physics

Lesson : Gravitation

Topic:Unit of weight

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