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Mechanics

Newton’s Laws of Motion

Law 1:

A body will continue in a state of rest or uniform motion unless acted on by an external force.

This is often called the law of inertia.

Law 2:

The net (or resultant) force acting on a body is equal to the product of its mass and its acceleration.

  Force = mass × acceleration
  SF = ma

Law 3:

If body A exerts a force on body B, then body B exerts an equal but opposite force on body A.

The symbol means "the sum of" so, if we have two forces and , acting on a body, then means .

So, remember, represents a vector addition.

For example:

 The sum of these two forces is found by vector addition.

If the two forces act along the same line then the arithmetic becomes a little easier.

In this case, SF is equal to
+10 – 4 = 6 N (to the right)

Using Newton’s Second Law of Motion

An object of mass m = 20kg rests on a horizontal surface. Calculate the magnitude of the force exerted by the surface on the object in the following situations.

a) Stationary or moving with constant velocity

 F = ma

also, F = R + mg

but, in this case a = 0

therefore, R + mg = 0

and so R = -mg

R = 196 N

b) Accelerating upwards at 2 ms-2

 F = ma

also, F = R + mg

therefore, 
R + mg = ma

and so R = m(a – g)

R = 236 N

c) Accelerating downwards at 9·8 ms-2

 F = ma

also, F = R + mg

therefore, 
R + mg = ma

and so R = m(a – g)

R = 0

So, in this case, the body would appear to be weightless.

 

© David Hoult 2008