How Does Time Influence Velocity in Different Scenarios?

[Misr]

My book
If an egg falls from a height to a metal surface it surely smashes but if it falls from the same height onto a cushion it doesn't smash although the linear momentum and consequently the impulse is the same since the terminal velocity of the egg is zero in both cases.
The reason for this is the contact time when the egg hits the metal surface is so short and then the force is great sufficient to break the egg.

although the linear momentum and consequently the impulse is the same since the terminal velocity of the egg is zero in both cases.

Why??

1- A tennis player is aware that he must appky a follow through to elongate the time interval in which the ball is in contact with the racket.This increase the impulse and hence the velocity is increased to cover a larger distance.

Why does the time affect velocity in this case not force (as in first case)?

Thanks

 

[LostConjugate]

The first example is acceleration or total force. If the egg accelerates faster, as it does when it stops quickly on the metal plate, the force is greater.

The tennis player example is Force over time. If the tennis player put a stronger force they could get the same velocity with a shorter contact time.

 

[Misr]

I dun think this really helped
I asked why does the linear momentum / impulse equal in both cases ?
and

Why does the time affect velocity in this case not force (as in first case)?
I know that force is inversly proportional to time
So do u have a better explanation?
Thanks

 

[Borek]

I asked why does the linear momentum / impulse equal in both cases ?

I would say by definition. How is impulse defined? What is momentum change in both cases?

 

[Misr]

In the case of metallic plate
The linear momentum of the egg before collision is mV1
The linear momentum of the egg after collision is zero (since the terminal velocity is zero)

In case of cushion:
The linear momentum of the egg before collision is mV2
The linear momentum of the egg after collision is zero (since the terminal velocity is zero)

and according to the law of conservation of linear momentum :
mV1 = mV2
and force is inversely proportional to time when the change of linear momentum is constant

but in the second case the change in linear momentum is not constant so time doesn't affect force

right or wrong?

 

[Borek]

Momentum of the egg before collision is in both cases identical - mV, so no need for V1 & V2.

You have dodged my question about impulse definition and it is crucial for the answer.

 

[russ_watters]

Why does the time affect velocity in this case not force (as in first case)?

In the first case, the egg case (two cases, really), the velocity is provided by a fall under gravity, so it is equal...it is essentially a starting condition of the problem, and not something to be investigated in the problem.

In the tennis racket case, the velocity is variable because its the entire thing being investigated in the two cases.

Basically, the two examples are examining opposite sides of the same coin: The first example examines how force can be altered by increasing the contact time and the second example examines how impulse can be altered by increasing contact time.