I came up with this experiment in my head. Suppose there are two blocks $A$ and $B$ in an ideal situation(no friction, gravity, air resistance whatsoever).
Velocity of $A$($v_A$)=$10 ms^{-1}$
Velocity of $B$($v_B$)=$0 ms^{-1}$
Mass of $A$($m_A$)=$2kg$
Mass of $B$($m_B$)=$5kg$
After $A$ hits $B$, $B$ gains an acceleration of $2ms^{-2}$. So the force acting on $B(F_A)=(5×2)=10N$, and due to Newton's Third Law, force acting on $A(F_B)=-10N$.
$\therefore$ acceleration of $A(a_A)=\frac Fm = -5ms^{-2}$
Lets suppose the time for which the force acted between the two, i.e., the contact period between the two bodies $A$ and $B$ is $t$ $s$.
Hence, for $A$, final velocity $$v_A=u+at=(10-5t)ms^{-1}$$
And similarly for $B$, final velocity
$$v_B=(0+2t)ms^{-1}=(2t)ms^{-1}$$
If $t$ is very small, then obviously $$v_A>v_B$$
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Does this mean that the objects will not separate from each other after coming in contact, as the object $A$ is constantly approaching $B$ with a velocity of $v_A-v_B$?
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But this means that $v_A$ is constantly applying a variable(decreasing) force on $B$ overtime as the relative velocity of $A$ with respect to $B$ is decreasing as time passes and eventually when $v_A-v_B$ becomes $0$($\because$ $v_A$ is decreasing and simultaneously $v_B$ is increasing), the no force act on any of them and they move with uniform velocity(dynamic equilibrium)?
I might be wrong, as I was overwhelmed with this thought experiment(I am only in 10th grade so I have a very limited knowledge of physics compared to the usual users on this website). I would like some clarifications and some maths behind my assumptions, if possible.
Best Answer
Assuming the blocks are elastic, when the lighter block hits the heavier one, the two momentarily compress then uncompress and come apart. It is that interaction that transfers momentum and energy from the lighter block to the heavier one.
The situation you describe in which the velocity of the lighter block exceeds the velocity of the heavier one is true up to the end of the compression stage. As you imagined, the velocity of the lighter block gradually reduces and the velocity of the heavier one gradually increases until they are the same- at that point the two blocks stop coming closer together (ie the compression goes no further). However, your mistake is to assume they then move together in a state of equilibrium. Instead, from that point onwards, the stored up potential energy in the compressed blocks causes the blocks to expand, forcing them to move apart, further increasing the speed of the heavy block and further reducing the speed of the lighter block. The acceleration of the blocks ends when they lose contact with each other and go their separate ways.
Your thought experiment would be right in principle if the two blocks were inelastic and stuck together after their collision.