Force

  One of the most basic concepts of physical science is that of force. In classical mechanics, the mechanics originally formulated by Isaac Newton at the end of the seventeenth century, a body of mass m travels in a straight line at constant speed until a force acts on it. Then it undergoes an acceleration, a rate of change of velocity, given by Newton’s second law of motion:

Force= mass x  acceleration     F= ma

 The acceleration of a freely falling body at the surface of the Earth is 9.81 m s^-2, so the gravitational force acting on a mass of 1.0 kg is

F = (1.0 kg) x (9.81 m s^-2) = 9.8 kg m s^-2 = 9.8 N

The derived unit of force is the newton, N:

1 N =1 kg m s^-2

  Therefore, we can report the force we have just calculated as 9.8 N. It might be helpful to note that a force of 1 N is approximately the gravitational force exerted on a small apple (of mass 100 g).

Force is a directed quantity, in the sense that it has direction as well as magnitude.  For a body on the surface of the Earth, the force of gravitational attraction is directed toward the center of the Earth.

When an object is moved through a distance s against an opposing force, we say that work is done. The magnitude of the work (we worry about signs later) is the product of the distance moved and the opposing force:

Work = force x distance

Therefore, to raise a body of mass 1.0 kg on the surface of the Earth through a vertical distance of 1.0 m requires us to expend the following amount of work:

Work = (9.8 N) x (1.0 m)= 9.8 N m

As we shall see more formally in a moment, the unit 1 N m (or, in terms of base units, 1 kg m² s^-2) is called 1 joule (1 J). So, 9.8 J is needed to raise a mass of 1.0 kg through 1.0 m on the surface of the Earth.