# Definition of a force

## Main Question or Discussion Point

0k i know net force on a body is defined as mass times acceleration of the body w.r.t inertial frame,
but how do we define individual forces acting on the body?
Eg. Forces acting on a 1kg block are F1=+6¡ And F2=-4¡
So we know net force=2¡, and net acceleration=2 m/s^2
but how do we actually apply something called "6 N" force in right direction, and "4 N" in left direction?
Thank you.

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tiny-tim
Homework Helper
Hi Viru.universe!
Eg. Forces acting on a 1kg block are F1=+6¡ And F2=-4¡
So we know net force=2¡, and net acceleration=2 m/s^2
but how do we actually apply something called "6 N" force in right direction, and "4 N" in left direction?

If a force is applied to the body at a particular point, just trace it back to its source, and then the amount of the force will be obvious.

Eg, if a mass on a table is being pulled by two horizontal strings going over pulleys and joined to weights, then the individual force on each string is equal to that weight (ie the mass, times g).

Andrew Mason
Homework Helper
0k i know net force on a body is defined as mass times acceleration of the body w.r.t inertial frame,
but how do we define individual forces acting on the body?
Eg. Forces acting on a 1kg block are F1=+6¡ And F2=-4¡
So we know net force=2¡, and net acceleration=2 m/s^2
but how do we actually apply something called "6 N" force in right direction, and "4 N" in left direction?
Thank you.
Are you seeking a definition of the individual forces or just wanting to know how a constant force can be applied?

It is easy to imagine such constant forces in a static system. But it is not so easy to explain HOW such constant forces would be applied in a dynamic system.

The 4N force could be friction, which is always opposite to the direction of motion and is fairly constant regardless of speed. But the 6N force would have to be from something like a spring whose extension is maintained as the body accelerates.

AM

Yeah i am seeking definition for individual forces, i got examples how to apply constant force to a system

Chestermiller
Mentor
There are two sides to the equation. Force is not really defined as mass times acceleration. F = ma is really a definition of mass. ma goes on the left side of the equation, while, on the right side of the equation, you have the net force. This is the sum of all the "contact forces" on the body. A contact force is caused by the mechanical interaction of bodies that are pressing against one another or pulling on one another. Another kind of force is "body force" such as gravity, which also goes on the right side of the equation. GMm/r2 is regarded as a contributor to the acceleration. But ma in not equal to GMm/r2, unless gravity is the only force acting on the body.

I didn't understand
"F=ma is really a definition of mass"

Andrew Mason
Homework Helper
Yeah i am seeking definition for individual forces, i got examples how to apply constant force to a system
The individual force, F, if applied to an inertial body of mass m on which no other forces were acting, would cause that body to accelerate at a rate of a = F/m. That is how the force would be measured.

We define the concept of force in general terms. F = ma is not necessarily a definition of force. Force is defined in Newton's first law as that which is required to effect a change in the motion of a body. That is the definition of force. F = ma is a formula for determining the magnitude of the force.

Newton observed that the same push or pull applied for equal amounts of time to bodies of different mass caused equal changes in motion in each body, provided one defined the quantity of motion as the body's mass x its velocity. So it seems reasonable to define the magnitude of a force by the magnitude of the changes in motion its causes per unit time: F = dp/dt

AM

Chestermiller
Mentor
I didn't understand
"F=ma is really a definition of mass"
newton determined empirically that the acceleration of a body is proportional to the force applied to the body. Mass is the proportionality constant between the net force on a body and its acceleration. therefore, F=ma can be looked upon as a definition of the property of mass.

tiny-tim
Homework Helper
F = ma (Newton's second law) is not actually the original equation.

The original equation is I = ∆(mv), or impulse = change in momentum

Differentiating that gives dI/dt = ma + (dm/dt)v,

and if m is constant then the RHS is just ma.

We call dI/dt "force", and write it "F"

∆(mv) is easy to measure, and therefore so is I.

a is not so easy to measure (especially in equilibrium! )​