Question

Does anyone know how to calculate how many times a ball will bounce if dropped from some height?
Information:
Restitution = 0.85
Mass = 0.7 kg
Drop Height = 10 m
Gravity = 9.81 m/s
Ground is Horizontal.
No air resistance.

Answer 1

velocity of separation = e (velocity of approach)

Answer 2

A little more explanation please?

Answer 3

does it make sense?

Answer 4

why are you subtracting 0?

Answer 5

Velocity of approach = V' - zero...which is velocity of ground

Answer 6

sorry...Velocity of approach = V - zero...which is velocity of ground

Answer 7

ball is colliding with the ground..and use this velocity of separation = e (velocity of approach)

Answer 8

similarly velocity of separation = V'-0

Answer 9

okay. so e is the math constant..
what am i solving for?

Answer 10

so 1st calculate V, the velocity of ball from which it hits the ground 1st time..

Answer 11

no...e is the coefficient of restitution...and for ur problem e =0.85(given)

Answer 12

Potential Energy completely becomes Kinetic Energy just before collision
\[E_{system}=0+mgh=(0.7)(9.81)(10)=68.67\]\[E_{kinetic}=E_{system}\]\[v_{before}=\sqrt{2E_{kinetic} \over m}=14.01[ms^{-1}]\]\[\mu_r = {E_{kin. after} \over E_{kin.before}}\]\[E_{kin. after}=\mu E_{kin. before}=(0.85)(68.67)=58.67[J]\]\[v_{after}=\sqrt{2E_{kinetic} \over m}=12.91[ms^{-1}]\]

I have both the velocities. Before and after the bounce.

Answer 13

but see 4th line in ur solution..

Answer 14

The ball will bounce an infinite number of times, but the process will have a finite duration.

Answer 15

velocity of separation = e (velocity of approach)
it does not mean that... Energy after collision =e( energy before collision)?

Answer 16

That's one of the formula we were given.. that restitution is energy after divided by energy before. so i just used that to calculate energy after collision and then the velocity.

Answer 17

But the correct formula is for velocity not for energy
velocity of separation = e( velocity of approach)

Answer 18

http://scienceworld.wolfram.com/physics/CoefficientofRestitution.html
check this

Answer 19

So our professor gave us the wrong equation... awesome.

Answer 20

where are you from?

Answer 21

I'm studying in New Zealand.

Answer 22

ok

Answer 23

anyway...u can solve this problem by using correct formula

Answer 24

Wait, what do I do now that I've got the velocity before and after collision?
vel approach =14.01
vel separation = 11.91

Answer 25

yes...If u have done correctly...
Better use kinematics relation..and use symbols dont plug in the value now..just use h,g and all..then u'll get better understanding of this problem