# Force Measure

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A Force Measure is a physical measure of the rate of change of momentum with respect to time.

**Context:**- It is a vector quantity.
- It can be defined as:
- A physical quantity that can change the motion of an object.
- Newton's Second Law shows that force is acceleration multiplied by the mass of an moving object, i.e. [math]\displaystyle{ \vec{F} =m\vec{a} }[/math]. This is assuming object's mass is a constant, relativistic effects have to be taken into account when the moving object approches the speed of light.
- It is the derivative of the momentum with respect to time, [math]\displaystyle{ \vec{F}=d\vec{p}/dt }[/math].

- There are 4 fundamental forces in the Universe: gravitational, electromagnetic, nuclear strong and weak.

- The units of measurement of force are given by:

- [math]\displaystyle{ [Force]=\frac{[momentum]}{[time]}=\frac{[mass]\times[velocity]}{[time]}=\frac{[mass][length]}{[time]^2} }[/math]
- where [math]\displaystyle{ [x] }[/math] symbolizes the conversion of the quantity [math]\displaystyle{ x }[/math] to its units of measurement. Thus, the units of measurement for force in International System of Units is kilograms meters per squared seconds, which is defined as Newton Unit ([math]\displaystyle{ N = kg m/s^2 }[/math]).

**Example(s):****Counter-Example(s):**

**See:** Physical Body, Physical Mechanics Discipline, Inertia, Newton Unit, Net Force, External Force, Internal Force, Fundamental Force, Frictional Force, Gravitational Force, Nuclear Weak Force, Electromagnetic Force, Nuclear Strong Force, Newton's Second Law, Centrifugal Force, Acceleration, Velocity, Momentum, Pressure.

## References

### 2016

- (Wikipedia, 2016) ⇒ https://www.wikiwand.com/en/Force
- In physics, a force is any interaction that, when unopposed, will change the motion of an object. In other words, a force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate. Force can also be described by intuitive concepts such as a push or a pull. A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newtons and represented by the symbol F.

- The original form of Newton's second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time. If the mass of the object is constant, this law implies that the acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object
- Related concepts to force include: thrust, which increases the velocity of an object; drag, which decreases the velocity of an object; and torque, which produces changes in rotational speed of an object. In an extended body, each part usually applies forces on the adjacent parts; the distribution of such forces through the body is the so-called mechanical stress. Pressure is a simple type of stress. Stress usually causes deformation of solid materials, or flow in fluids.

### 2005

- (Hyperphysics Encyclopedia, 2005) ⇒ http://hyperphysics.phy-astr.gsu.edu/hbase/force.html#fordef
- QUOTE: One of the foundation concepts of physics, a force may be thought of as any influence which tends to change the motion of an object. Our present understanding is that there are four fundamental forces in the universe, the gravity force, the nuclear weak force, the electromagnetic force, and the nuclear strong force in ascending order of strength. In mechanics, forces are seen as the causes of linear motion, whereas the causes of rotational motion are called torques. The action of forces in causing motion is described by Newton's Laws under ordinary conditions, although there are notable exceptions.

- Forces are inherently vector quantities, requiring vector addition to combine them.
- The SI unit for force is the Newton, which is defined by [math]\displaystyle{ N = kg m/s^2 }[/math] as may be seen from Newton's second law.

### 1996

- (Wolfram Science World, 2005) ⇒ http://scienceworld.wolfram.com/physics/Force.html
- QUOTE: The concept of the force was essential to the development of mechanics and all of physics. A force is a "push" or "pull" experienced by a mass m when it is accelerated,

- [math]\displaystyle{ \vec{F}=m\vec{a} }[/math]
- which is Newton's second law (with a the acceleration). In a gravitational field with gravitational acceleration [math]\displaystyle{ g }[/math], a mass [math]\displaystyle{ m }[/math] therefore experiences a force

- [math]\displaystyle{ \vec{F}=m\;g }[/math]
- known as its weight.
- The SI unit of force is the newton, equal to 1
`kg m s^{-2}`

. The cgs unit of force is the dyne, and the British engineering unit of force is the pound (or, more explicitly, the pound-force). The kilopond is sometimes also used as a unit of force.

### 1963

- (Feynman et al., 1963) ⇒ Richard P. Feynman, Robert B. Leighton and Matthew Sands (1963, 1977, 2006, 2010, 2013) "The Feynman Lectures on Physics": New Millennium Edition is now available online by the California Institute of Technology, Michael A. Gottlieb, and Rudolf Pfeiffer ⇒ http://www.feynmanlectures.caltech.edu/
- QUOTE: Newton wrote down three laws: The First Law was a mere restatement of the Galilean principle of inertia just described. The Second Law gave a specific way of determining how the velocity changes under different influences called forces. The Third Law describes the forces to some extent, and we shall discuss that at another time. Here we shall discuss only the Second Law, which asserts that the motion of an object is changed by forces in this way: the time-rate-of-change of a quantity called momentum is proportional to the force.

- (...) Thus at the beginning we take several things for granted. First, that the mass of an object is constant; it isn’t really, but we shall start out with the Newtonian approximation that mass is constant, the same all the time, and that, further, when we put two objects together, their masses add. These ideas were of course implied by Newton when he wrote his equation, for otherwise it is meaningless. For example, suppose the mass varied inversely as the velocity; then the momentum would never change in any circumstance, so the law means nothing unless you know how the mass changes with velocity. At first we say, it does not change.
- Then there are some implications concerning force. As a rough approximation we think of force as a kind of push or pull that we make with our muscles, but we can define it more accurately now that we have this law of motion. The most important thing to realize is that this relationship involves not only changes in the magnitude of the momentum or of the velocity but also in their direction. If the mass is constant, then Eq. (9.1) can also be written as

- [math]\displaystyle{ F=m\frac{dv}{dt}=m\;a }[/math]