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Mechanisms
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Mechanisms
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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.
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Moment
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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.
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Medium force
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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.
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Model
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Parameters
Variables
Calculations
to 
, then, select the variable: 
to 
Calculations
Calculations
Variable 
Given Calculate 
Target : Equation To be used 
Equations
$ \Delta m_i = m_i - m_0 $
Dm_i = m_i - m_0
$ \Delta p = p - p_0 $
Dp = p - p_0
$ \Delta t \equiv t - t_0 $
Dt = t - t_0
$ \Delta v \equiv v - v_0 $
Dv = v - v_0
$ F \equiv\displaystyle\frac{ \Delta p }{ \Delta t }$
F = Dp / Dt
$ p = m_i v $
p = m_i * v
$ p_0 = m_0 v_0 $
p = m_i * v
ID:(15388, 0)
Moment (1)
Equation
The moment ($p$) is calculated from the inertial Mass ($m_i$) and the speed ($v$) using
| $ p = m_i v $ |
ID:(10283, 1)
Moment (2)
Equation
The moment ($p$) is calculated from the inertial Mass ($m_i$) and the speed ($v$) using
| $ p_0 = m_0 v_0 $ |
| $ p = m_i v $ |
ID:(10283, 2)
Momentum Difference
Equation
According to Galileo, objects tend to maintain their state of motion, meaning that the momentum
$\vec{p} = m\vec{v}$
should remain constant. If there is any action on the system that affects its motion, it will be associated with a change in momentum. The difference between the initial momentum $\vec{p}_0$ and the final momentum $\vec{p}$ can be expressed as:
| $ \Delta p = p - p_0 $ |
ID:(3683, 0)
Elapsed time
Equation
To describe the motion of an object, we need to calculate the time elapsed ($\Delta t$). This magnitude is obtained by measuring the start Time ($t_0$) and the the time ($t$) of said motion. The duration is determined by subtracting the initial time from the final time:
| $ \Delta t \equiv t - t_0 $ |
ID:(4353, 0)
Medium force
Equation
The force ($F$) is defined as the momentum variation ($\Delta p$) by the time elapsed ($\Delta t$), which is defined by the relationship:
| $ F \equiv\displaystyle\frac{ \Delta p }{ \Delta t }$ |
ID:(3684, 0)
Constant mass
Equation
If the inertial Mass ($m_i$) changes, the momentum is altered unless the speed varies inversely. Therefore, it is important to consider the variation of inertial mass ($\Delta m_i$), calculated using the difference with the initial mass ($m_0$) as follows:
| $ \Delta m_i = m_i - m_0 $ |
ID:(15537, 0)
Speed variation
Equation
Acceleration corresponds to the change in velocity per unit of time.
Therefore, it is necessary to define the speed Diference ($\Delta v$) in terms of the speed ($v$) and the initial Speed ($v_0$) as follows:
| $ \Delta v \equiv v - v_0 $ |
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