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This is more of a confirmation post whether my ideas are correct or not.

Suppose a ball of mass $5 kg$ travelling with uniform velocity $5 ms^{-1}$ through vacuum hits a block of mass $200kg$ with force $F_a$. The wall gets an acceleration of $0.5ms^{-2}$.

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So the force acting on the block, i.e., $$m_{block}a_{block}=200×0.5 N=100N$$ Now I think the block will apply an equal reaction force on the ball $F_r$ which is equal to $ma$ as well, except that the mass of the ball is $5kg$, so the acceleration produced is $$a_{ball}=\frac {F_{r}}{m_{ball}} = \frac{-100}{5}=-20ms^{-2}$$

Now considering the equation of motion, we get $v=u+at$ the new velocity of the ball is: $$v=5-200t$$ right? So now if the ball is in vacuum, and energy loss due to heat and sound is $0$, If my above statements are correct, then the ball should have a retardation right? Like as soon as it touches the block, it slows down and eventually comes to rest. The retardation still acts on it so it now gains a velocity backwards. It will now keep moving backwards with an acceleration $200ms^{-2}$ right?

Now in practical situations, the ball will lose some energy on hitting the wall because of friction and heat. Now after the ball gets a negative acceleration, it will try to move back, but I have noticed that the ball won't move back much and fall down.

  • Is it because of gravity pulling it back, and resistance provided by air, which counteracts the movement of the ball and causes it to slow down and eventually stop?

  • Does this mean that it is not necessary that the object has to be compressible, as in a rubber ball, in order to bounce, as they follow Newton's Third Law anyways?

  • What would have happened if the ball was accelerating as well? Would the final motion of the ball be in the direction of the net acceleration?

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this question is impossible, the situation you've described isn't the full collision story , whilst the ball is hitting the block, it applies a force for SHORT time such that the change of momentum of the ball is F t where t is the duration of force application. once the ball is away from the block, no forces act in the ball and should travel with a CONSTANT velocity. if your scenario specified the acceleration and DURATION of the collision then it makes sense, as if it applies a force for a time it has some change in momentum, and then you can use conservation of MOMENTUM to find the velocity of the ball

Take away, It moves at a constant velocity, collisions happen for a short time and applies a force for a short time

Search up "impulse" $\int F dt$ = Change in momentum

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