Respuesta :
Answer:
[tex]\Delta P = F \Delta t[/tex]
Explanation:
As we know Newton's II law
[tex]F [/tex]= Rate of change in momentum
so we will have
[tex]F = \frac{\Delta P}{\Delta t}[/tex]
now we will have
[tex]\Delta P = F \Delta t[/tex]
so here we can say that change in momentum of the object is the product of force and interval of time for which the force is acting on it.
so we will have
[tex]\Delta P = F \Delta t[/tex]
The magnitude of resultant change in momentum can be given by the expression
Δp = m [tex]\times[/tex][Δ (Δx/Δt)]/Δt
Given that a force has constant magnitude
Let the magnitude of force = F Newton
From second law of Newton we can write as given by equation (1)
[tex]\overrightarrow{F} = m\overrightarrow{a}[/tex]....(1)
Where [tex]\overrightarrow{F} = Vector \; sum\; of \; All \; external\; forces \; acting \; on \; the\; system \\[/tex]
m = mass of the system
[tex]\overrightarrow{a}[/tex]= acceleration of center of mass of the system
Considering only magnitudes for the ease of problem solving
F = m a ( Given F is constant )
which can be written as equation (2)
F = [tex]m \times \dfrac{dv}{dt}[/tex]..........(2 )
F = mv /Δt ( as initial velocity= 0 )
since mass remains constant we can write
F = [tex]\dfrac{d(mv) }{dt }[/tex]
F = [tex]\dfrac{dp}{dt}[/tex]........(3)
equation (3) clearly states that rate of change of momentum is equal to
Net external force acting on the system.
So we can write F = Δ p/Δt.......(4)
also Δp = m[tex]\times[/tex](Δv/Δt) .....(5)
and v = Δx/Δt.......(6)
so from equation (5) and (6) we get
Δp = m [tex]\times[/tex][Δ (Δx/Δt)]/Δt
For more information follow the link below
https://brainly.com/question/13447525
