Newton's Second Law

This law is all about the situation when there is a resultant force and therefore there is also an acceleration.



You need a force to change the motion of a body. The bigger the net force the greater the acceleration. (remember that force is a vector and the direction of the forces acting on a body need to be considered). Aristotle thought that the force was in the same direction as the motion (i.e. the velocity). This is not true - the force is in the same direction as the acceleration if you don't follow this think of a basket ball being thrown into a net. the ball follows a curving path in the air but the force - and therefore the acceleration is always in one direction - vertically downwards.

You can investigate the law practically by using a linear air track and measuring the acceleration of the truck for a variety of accelerating forces and truck masses. The linear air track is the best equipment to use since the force of friction is very low.
It is also important to remember that the mass being accelerated is the total mass of the truck plus the mass of the accelerating weight although this is not significant if the truck is very heavy in comparison. The results can be analysed by plotting two graphs - one of the acceleration against the accelerating force and the other of acceleration against the inverse of the mass of the truck (1/m)

This should show you that the :
(a) acceleration is directly proportional to the accelerating force and
(b) acceleration is inversely proportional to mass of the body being accelerated
Combining these two results gives



The units for force are Newtons (N), mass are kg and acceleration ms^-2.
This law also gives us a good definition of the Newton as a unit of force.



Although we may think of the second law as "Force equals Mass times Acceleration" Newton actually stated his famous law as follows:-



Expressed mathematically Newton's Second Law is:

Force = d(mv)/dt

now if mass is constant then F = d(mv)dt = mdv/dt = ma - consistent with the simple statement of the law.