0.17 Phy1150: force and motion -- units of force  (Page 5/9)

A dyne is a unit for force that causes a mass of one gram to accelerate at one centimeter per second squared (1 cm/s^2). Once again, we can convert backand forth between dynes and newtons using the following relationship:

1 dyne = 0.00001 newton

Acceleration of gravity

The values for the next three units of force that I will explain depend on the gravitational attraction between the earth and other objects.

The universal law of gravitation tells us that objects having mass are attracted to one another by a force that is proportional to the product oftheir masses and inversely proportional to the distance between them.

attractive force = G*m1*m2/d^2

where

• G is the gravitational constant 6.673*10^(-11)*m^3*kg^(-1)*s^(-2)
• m1 and m2 are the masses involved
• d is the distance between the masses

It is also true that for large spherical masses like the earth, the effect is as if all of the mass is concentrated at a point located at the center of thesphere.

Objects are attracted to the earth

Therefore, all objects on or near the surface of the earth are attracted toward the center of the earth by an amount given by the above equation .

Neglecting friction such as air resistance, objects near the surface at different points on earth fall with an acceleration somewherebetween about 9.78 m/s^2 and 9.82 m/s^2 depending on latitude.

pound-force

The unit of force named pound-force incorporates the gravitational pull of the earth in its definition. One pound-force is the force required to cause a mass of onestandard pound to be accelerated by an amount equal to the standard acceleration of gravity that exists near the surface of the earth.

In accordance with the General Conference on Weights and Measures , standard gravity is usually taken to be 9.80665 m/s^2 (32.174049 ft/s^2).

The acceleration of the standard gravitational field and the international avoirdupois pound define the pound-force as:

• 1 pound-force = 1 pound * 32.174049 ft/s^2
• 1 pound-force = 0.45359237kg * 9.80665 m/s^2
• 1 pound-force = 4.44822162 newton

gram-force

As with pound-force, the unit of force named gram-force also incorporates the gravitational pull of the earth in its definition. One gram force is the force required to cause a one-gram mass to beaccelerated by 980.665 cm/s^2.

We can convert force back and forth between units of gram-force and units of newton using the following relationship.

1 gram-force = 0.00980665 newton

kilogram-force

Finally, the unit of force named kilogram-force also incorporates the gravitational pull of the earth in its definition. One kilogram-force is the force required to cause a one-kilogram mass to beaccelerated 9.80665 m/s^2.

Once again, we can convert between force units of kilogram-force and newton using the following relationship.

1 kilogram-force = 9.80665 newton

Weight is a force

Despite the fact that scales in the grocery stores in the United States have displays that read in pounds (which is a unit of mass), weight is not a measureof mass. Weight is a measure of force.

What exactly is the weight of an object?