Aforce of constant magnitude f and fixed direction acts on an object of mass m that is initially at rest. if the force acts for a time interval ∆t over a displacement ∆x , what is the magnitude of the resultant change in the linear momentum of the object?

Explanation:

As we know Newton's II law

= Rate of change in momentum

so we will have

now we will have

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

The magnitude of resultant change in momentum can be given by the expression

Δp = m [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)

....(1)

Where

m = mass of the system

=  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 =  ..........(2 )  

F = mv /Δt  ( as initial velocity= 0 )

since mass remains constant we can write

F =

F =  ........(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(Δv/Δt) .....(5)

and   v = Δx/Δt.......(6)

so  from equation (5) and (6) we get

Δp = m [Δ (Δx/Δt)]/Δt  

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think about the oscillation of the toy shown in the video. when the toy is at the highest point of its motion, its velocity is zero and its acceleration is negative.

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