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Experimental Verification of Newton's Second Law of Motion
It is observed that if a mass, m, causes a given spring to extend x, then 2m causes 2x and 3m causes 3x etc. See diagram below.
We conclude that the force due to gravity exerted by a suspended mass m is proportional to the mass.
The mobile moves without friction on a cushion of air.
As we have three variables, force, mass and acceleration, the investigation must be done in two parts.
To find the relation between acceleration and force with mass constant.
The force is provided by gravity.
To maintain a constant mass whilst varying the force, masses, m were moved from the mobile to the string as shown below.
In this experiment, the same object was pulled by forces of different magnitudes. The acceleration produced by each force was measured.
The body being accelerated started from rest so we can write
These two equations can be combined to eliminate t which then gives us
So, to measure the acceleration of the body we measured its velocity, v, after it had been accelerating for a known distance, s.
We did not know the magnitudes of the forces but we did know how the force varied.
These results show that the acceleration is directly proportional to the force.
To find the relation between acceleration and mass with force constant.
In this experiment, an object was pulled with a certain force and the acceleration was measured as before. The mass of the object was then increased and it was pulled again with the same force.
These results show that the acceleration is inversely proportional to mass.
The two conclusions can be combined in one statement
so, written as an equation we have
and if we choose the units correctly the constant can be made equal to 1. Therefore, we have
This is know as Newton’s second law of motion.
The "correct" units are
This relation therefore gives us a definition of the unit of force.
Also, if we rearrange the equation to give
we are reminded that the mass of a body is a measure of its inertia.
This is clear because if m is large, a large force is needed for a given acceleration.