squash ball
the coefficient of restitution of the squash ball is about 20%... that is... if 100J is given to the ball it would release 20J as mechanical energy and the rest will be dissipated as heat (entropy)...the squash ball would have to serve as an energy storage device... the batsman would give energy to the squash ball by compressing it before the cricket ball hits the bat and would allow the ball to expand when the cricket hits the bat...
in terms of physics is see no other way that the squash ball would serve to assist the batsman other than it being a device that would increase the comfort factor... and the batsman obviously gets a better grip and that makes him deliver more power.... also aussies have big palms so the ball def gave him a better grip!!!
on the contrary... if the timing is wrong squash ball would server as a damper... absorbing 80% of the energy of the impact when the ball hits the bat! this would be disadvantageous in terms of energy to the batsman! because the squash ball has a low coefficient of restitution (20%)... so if the squash ball wasnt present... that 80% loss would not be there!
so i seriously doubt that gilchrist had all this in mind when he stuck the squash ball up his gloves! it would have been to get a better grip... or hey... may be he didnt have the balls to face malinga... hehe
but now that we're talking about the dynamics of it... lets just analyze it in a very crude way...
lets look at it in terms of energy
you can do a simple calculation to find out how much energy a cricket ball has when it leaves the bat...t - time of flight: that is the time when the ball hits the bat till it falls on the ground
v - velocity vector of the ball leaving the bat
m - mass of the ball (163g)
we will make the following assumptions
aerodynamic forces acting on the ball is neglected...
and that the trajectory of the ball is a true parabola
energy, E=½mv2 ---(1)
maximum distance, d=v2/g ---(2)
from (1) and (2): E=½mdg ---(3)
so if the ground radius is 75m and we try to clear the rope by about 10m:
d=85 and from (3) we get E=68J
the bat
the maximum coefficient of restitution of a cricket bat is about 70%... the energy delivered from the bat comes partly from kinetic energy of the cricket ball and of course from the batsman...fast balls
a cricket ball traveling at 120 km/h (33m/s) would have around 90J of kinetic energy... so 70% of 90J is 63J... and thats 5J short of 68J needed to clear the ropes... so the batsman just needs to add another 7J and thats not much... unless you're like 5 or somethihng!
slow balls
a cricket ball traveling at 80 km/h (22m/s) would have around 50J of kinetic energy... and 70% of that is 35J... so the batsman has to add another 33J to the cricket ball match the 68J needed to clear the ground... so thats 47J that the batsman must add to the bat...
how much is 47J? well 100J is the amount of energy that a paramedic would give to a person who is not breathing... and its not much... a 100J punch woudlnt even hurt you that much... you'd go "ouch" for a few seconds and thats it...
i hope this was useful...
