k in f=ma
Name: Ki Y.
In the f=ma equation we have taken f~m & f~a .Then we get f=k(ma).
How can we take k=1.By practically? or is the definition of the force says it.
Remember, the force f, the mass m, and the acceleration a are all
dimensioned quantities, that is they have "units". The mass for example has
units of mass e.g. kilograms, pounds. The acceleration has units of
meters/(sec^2) , feet/(min^2) etc. and so on. So the numerical value we
assign to let's say the force, f, depends upon which units of mass and
distance we use to do the measurement or do the computation.
We set the proportionality constant by defining units to make it so. In
metric units, the "Newton" is defined as the force that will give 1 kilogram
of mass an acceleration of 1 m/s^2. This sets the constant to 1 if you use
m/s^2 for acceleration, kilograms for mass, and Newtons for force. In the
British system, a common acceleration is feet/sec^2. The common force is
pounds. The mass unit is called a slug. 1 slug is the mass to which 1
pound of force provides an acceleration of 1 ft/s^2. Physicists try to
define their units for convenience. F=ma is much more convenient than
Dr. Ken Mellendorf
Illinois Central College
Click here to return to the Physics Archives
Update: June 2012