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Force
Storyboard

To change the state of a body, one must change its momentum.The rate at which this occurs is called force, defined as the change in momentum over time and is a vector since the change in momentum is. Newton defined this in his second principle.

>Model

ID:(597, 0)


Mechanisms
Concept


ID:(15470, 0)


Isaac Newton
Description

Newton was the first to establish the basic principles that enable us to understand motion. His work, "Principia Mathematica," summarizes three fundamental laws that allow us to calculate how bodies move.

The foundation of his thinking lies in the concept of change in momentum over time, which he refers to as force. In the absence of force, momentum remains constant, resulting in an unaltered velocity when mass is constant. Additionally, Newton conceived the idea that forces occur in pairs; for a force to exist, its opposite reaction must also exist. These principles, known as Newton\'s laws of motion, laid the groundwork for classical physics and remain essential for understanding the behavior of objects in motion.

ID:(636, 0)


Moment
Concept

If we consider a body with mass $m$ and velocity $v$, it can be seen that there are two situations in which it is more difficult to change its motion:

• its mass is very large (for example, trying to stop a car)
• its velocity is very high (for example, trying to stop a bullet)

Therefore, a measure of motion that takes into account the body is introduced as the product of mass and velocity, which is called the body's momentum.

It is defined as:

$$

ID:(15477, 0)


Concept of force
Concept

Force is responsible for generating motion, particularly in the case of translation. Conceptually, it can be understood as the speed at which momentum is added (or subtracted) to a body.

ID:(1069, 0)


Medium force
Concept

To estimate the displacement of an object, it's essential to understand how its momentum varies over time. Therefore, the ratio between the momentum variation ($\Delta p$) and the time elapsed ($\Delta t$) is introduced, defined as the force ($F$).

To perform the measurement, we can work with a system like the one shown in the image:



To determine the average force, a dynamometer is used, which consists of a spring that, when extended under the effect of the force, indicates on a scale the intensity of it.



The equation that describes the average force is:

$ F \equiv\displaystyle\frac{ \Delta p }{ \Delta t }$



It should be noted that the average force is an estimation of the real force. The main problem is that:

The momentum varies during the elapsed time, so the value of the force can be very different from an average force.



Therefore, the key is to

Determine the force in a sufficiently short elapsed time so that its variation is minimal.

ID:(15476, 0)


Principia
Description

Newton\'s theories were made public in his book "Philosophiæ Naturalis Principia Mathematica".

This book, commonly known as "Principia," is considered one of the most important works in the history of science. In it, Newton presents his laws of motion and the law of universal gravitation, laying the foundations of classical physics. The "Principia" revolutionized our understanding of the physical world and provided a mathematical framework for describing and predicting the motion of objects in the universe.

ID:(11531, 0)


Model
Concept


ID:(15388, 0)


Force
Model

To change the state of a body, one must change its momentum. The rate at which this occurs is called force, defined as the change in momentum over time and is a vector since the change in momentum is. Newton defined this in his second principle.

Variables
Symbol
Text
Variable
Value
Units
Calculate
MKS Value
MKS Units
$F$
F
Force
N
$m_i$
m_i
Inertial Mass
kg
$m_0$
m_0
Initial mass
kg
$p_0$
p_0
Initial moment
kg m/s
$v_0$
v_0
Initial Speed
m/s
$p$
p
Moment
kg m/s
$\Delta p$
Dp
Momentum variation
kg m/s
$v$
v
Speed
m/s
$\Delta v$
Dv
Speed Diference
m/s
$t_0$
t_0
Start Time
s
$t$
t
Time
s
$\Delta t$
Dt
Time elapsed
s
$\Delta m_i$
Dm_i
Variation of inertial mass
kg

Calculations

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Symbol
Equation
Solved
Translated

Calculations

Symbol
Equation
Solved
Translated

 Variable   Given   Calculate   Target :   Equation   To be used


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Examples


(ID 15470)

Newton was the first to establish the basic principles that enable us to understand motion. His work, "Principia Mathematica," summarizes three fundamental laws that allow us to calculate how bodies move.

The foundation of his thinking lies in the concept of change in momentum over time, which he refers to as force. In the absence of force, momentum remains constant, resulting in an unaltered velocity when mass is constant. Additionally, Newton conceived the idea that forces occur in pairs; for a force to exist, its opposite reaction must also exist. These principles, known as Newton\'s laws of motion, laid the groundwork for classical physics and remain essential for understanding the behavior of objects in motion.

(ID 636)

If we consider a body with mass $m$ and velocity $v$, it can be seen that there are two situations in which it is more difficult to change its motion:

• its mass is very large (for example, trying to stop a car)
• its velocity is very high (for example, trying to stop a bullet)

Therefore, a measure of motion that takes into account the body is introduced as the product of mass and velocity, which is called the body's momentum.

It is defined as:

$$

(ID 15477)

Force is responsible for generating motion, particularly in the case of translation. Conceptually, it can be understood as the speed at which momentum is added (or subtracted) to a body.

(ID 1069)

To estimate the displacement of an object, it's essential to understand how its momentum varies over time. Therefore, the ratio between the momentum variation ($\Delta p$) and the time elapsed ($\Delta t$) is introduced, defined as the force ($F$).

To perform the measurement, we can work with a system like the one shown in the image:



To determine the average force, a dynamometer is used, which consists of a spring that, when extended under the effect of the force, indicates on a scale the intensity of it.



The equation that describes the average force is:

$ F \equiv\displaystyle\frac{ \Delta p }{ \Delta t }$



It should be noted that the average force is an estimation of the real force. The main problem is that:

The momentum varies during the elapsed time, so the value of the force can be very different from an average force.



Therefore, the key is to

Determine the force in a sufficiently short elapsed time so that its variation is minimal.

(ID 15476)

Newton\'s theories were made public in his book "Philosophi Naturalis Principia Mathematica".

This book, commonly known as "Principia," is considered one of the most important works in the history of science. In it, Newton presents his laws of motion and the law of universal gravitation, laying the foundations of classical physics. The "Principia" revolutionized our understanding of the physical world and provided a mathematical framework for describing and predicting the motion of objects in the universe.

(ID 11531)


(ID 15388)

ID:(597, 0)