Is Ball Bouncing on a Surface a Simple Harmonic Motion?

[PhysicStud01]

Homework Statement

Why does the graph have this shape?

Relevant Equations

area under the graph gives the change in momentum

Answer is C.

 

[Bystander]

Answer is C.

..., and your question is...?

 

[PhysicStud01]

why is the shape of the force extension graph this way?

area gives change in momentum.
but the gradient does not represent any physical quantity?

why does the force increase at a decreasing rate, then decrease at an increasing rate?

 

[Bystander]

Step at a time: what is happening?

 

[PhysicStud01]

the ball has an initial velocity down.
this is reduced to zero, then increase upwards.

but does the force change this way? is it not constant? and why with this gradient?

 

[kuruman]

The force is zero just before contact is made, it is also zero immediately after contact is lost and is non-zero in between. Which of the 4 graphs best shows this?

 

[PhysicStud01]

The force is zero just before contact is made, it is also zero immediately after contact is lost and is non-zero in between. Which of the 4 graphs best shows this?

thanks, I had already understood this one.
but during the contact, why does the force behave this way?

 

[kuruman]

thanks, I had already understood this one.
but during the contact, why does the force behave this way?

How else can it behave if it is zero at the beginning and the end of the time interval? It has to reach a maximum in between. The idea is that the rubber ball and the table surface deform elastically while they are in contact. The force that one exerts on the other increases as the deformation increases, it is maximum at maximum deformation and decreases as the deformation decreases. Now if you are asking about the specific shape of the curve, that depends on the model used to describe the deformation, however all models will have the same general feature which distinguishes (c) from all the other answers.

 

[PhysicStud01]

How else can it behave if it is zero at the beginning and the end of the time interval? It has to reach a maximum in between. The idea is that the rubber ball and the table surface deform elastically while they are in contact. The force that one exerts on the other increases as the deformation increases, it is maximum at maximum deformation and decreases as the deformation decreases. Now if you are asking about the specific shape of the curve, that depends on the model used to describe the deformation, however all models will have the same general feature which distinguishes (c) from all the other answers.

so, it could be straight lines too? as long as it starts from zero, reach a maximum, then decreases to zero again?

 

[kuruman]

It could be as an approximation. Nature almost always abhors sharp corners which means that the slope of the F vs. t curve should be continuous at all points.

 

[PhysicStud01]

ok, thanks

 

[haruspex]

so, it could be straight lines too? as long as it starts from zero, reach a maximum, then decreases to zero again?

The ball is elastic, so to a first approximation it should be SHM. That makes it the positive half of a sine wave.