Question

The height of rebouncing of a ball from a fixed surface is given by h1=e^2h0,h2=e^4h0 and so on.... Why mass and air resistance is not affecting that height

Answer 1

@arjunrc143 could you please elaborate the symbols you so used I mean I am not getting the 0 is referring to. Would you please explain. :)

Answer 2

h1=First Rebounded Height
h0=Initial Height
e=coefficient of restitution
^=to the power

Answer 3

\[h _{1}=e ^{2}h_{0}\]

Answer 4

from "that height" you referred that the gravity and the air resistance is not effecting the ball to attain a particular height each time....... Am i right ?

Answer 5

yes:
By the equation only initial height and coefficient of restitution (e) is affecting the rebounded heiht.... But what if 2 substances of different masses is dropped

Answer 6

The one with more mass will fall fast as from the equation F=mg where g is the acceleration due to gravity, so it is dependent on the mass. So, the one with more mass will fall fast.

@arjunrc143 did you get the concept ? :)

Answer 7

oh...So velocity will more for body with more mass right.... now what about air resistance and the nature of material and surface

Answer 8

You can test this theory by taking a tennis ball and a golf ball and standing on a table. Hold your arms out at the same height and drop the objects. If your arms are held at the same height the balls will hit the ground at the same time. The times when this would not occur is if one object is flat paper and the other object is a ball. The paper will have more resistance because of its shape.

Answer 9

the velocity of an object under free fall depends both on the mass and the air resistance.

cause we cannot expect a feather and a ball to fall at the same time and we cannot take into granted that a golf ball will fall faster than a tennis ball. The velocity shall be dependent both on the AIR RESISTANCE AND THE MASS.

Answer 10

ty...

Answer 11

But if we are dropping a bouncing ball of mass m and another ball of same mass but with different material from a height h ; It is sure that bouncing ball will attain greater height..... Here air resistance is same for both .... So what happens here.....

Answer 12

"The one with more mass will fall fast as from the equation F=mg where g is the acceleration due to gravity, so it is dependent on the mass. So, the one with more mass will fall fast."

that is so horribly wrong! o.O
what are you saying man?! o.O o.O

Answer 13

Air resistance formula

Answer 14

If we compare a ball and a feather than, I am saying for that.

Answer 15

If you neglect air resistance, then all masses fall at the same rate..

if you consider air resistance, then the time of fall depends on shape and mass.. (air resistance is alittle complicated)

Answer 16

All the things I said was with air resistance and with the action of atmospheric drag force the velocity of two things shall surely depend on the mass. apologies if I was not able to suite with proper explanation at the initials.

Answer 17

apologies " air resistance OR with the action of atmospheric drag"

Answer 18

u said F = mg, so more m, more F, and all that

although you are right, that higher mass has higher Force (weight in this case), but since they have bigger inertia.. they fall at same rate!!
so all objects have same g ..

Answer 19

@arjunrc143
For the original question

air resistance does effect the height, but in your case, its been neglected

and since air resistance is neglected, mass doesn't come into the picture.. because like i said, in absence of air, all masses fall at same rate!

Answer 20

@Mashy @praxer So is there any equation for the rebounded height by considering the air resitance, Mass of the material, Nature of material and surface

Answer 21

@arjunrc143
Coefficient of restitution depends on material, nature etc.
and drag forces are really complicated..
and so if you try to do the physics, the complications will be enormous.. (usually scientists use computers to solve it)

and its useless, cause the approximation done in your formula is very close to the real world cases.. !

Answer 22

75 % satisfactory

Answer 23

lol what ?! xD

Answer 24

here; \[e=-(v \div u)\] since mass of surface is infinity and its initial and final velocities are zero. Negative sign the direction

Where are the other factors in the equation nature of material mass etc

Answer 25

e is a constant.. that depends on nature and material etc

depending on e, v is decided..

Answer 26

velocity of approach \[\alpha\] Velocity of separation

so velocity of approach = constant (e) * velocity of separation
right??

Answer 27

no its the other way around

velocity of seperation = constant (e) times velocity of approach

if e = 0.. velocity of seperation is zero (mud sticking to ground)
if e = 1 velocity of seperation = velocity of approach (perfect elastic ball maybe)

Answer 28

ty

Answer 29

Wc

Answer 30

@Mashy See this paper shows that e varies with v ,, Not the other way

Answer 31

COR = 1 – (0.18±0.07) (vi)
(0.5±0.1)

CoR is the coefficient of restitution and Vi is the initial. The only thing i understood was this. :)

Answer 32

@arjunrc143 thanks for sharing the journal.. :)