Monday, May 12, 2014

Tracker: dianielleteo student video squash ball motion

Tracker: dianielleteo student video squash ball motion
physics of squash ball model
x = if(t<0.168,-1.216E-2-9.791E0*t,-1.59+2.669E0*(t-0.168)+3.257E-1*(t-0.168)^2)
y = if(t<0.168,-9.744E-4+3.769E0*t,0.61+1.308E0*(t-0.168)-4.001E-1*(t-0.168)^2)
author of video: dianielleteo
author of model: lookang



video is well taken, fixed camera view point.


well tracked by student,
calibration done, but changed to 1.6 m from 160 cm.


To analyse the motion after hit by racket to wall and projectile away
physics that can be illustrated

Physics Performance Question: 

What model(s) can be used to describe the motion of the squash ball after hit by racket and is subsequent motion bouncing off the squash court wall and what physics can be suggested-discovered from this analysis and model?

you can try to build kinematics model using the equations as follow
x = if(t<0.168,-1.216E-2-9.791E0*t,-1.59+2.669E0*(t-0.168)+3.257E-1*(t-0.168)^2)
y = if(t<0.168,-9.744E-4+3.769E0*t,0.61+1.308E0*(t-0.168)-4.001E-1*(t-0.168)^2)

Logic of model

where the logic of the if statement(model) is
if ( test , true do this, false do that)
contextually speaking
if ( t less than 0.168 s, the model is $ x = x_{0} + u_{x}t $, else t > 0.168 s, the model is $ x = x2_{0} + u2_{x}t_{2} + a_{x2}t_{2}^{2}$,
where $  t_{2} = (t -0.168) $ because this part 2 of the model requires a shift in the t axis.
similarly for y you can follow the logic.

Possible Physics demonstrated 

there appears to have a small $ a_{x} = 0.3257 \frac {m}{s^{2}} $ in order of the model to fit the real motion, which suggests the real motion of a squash ball after bouncing off the wall in this case, did have a small horizontal acceleration  $ a_{x} = 0.3257 \frac {m}{s^{2}} $. This is an unusual find from the typical physics taught in school, as most would assume $ a_{x} = 0 \frac {m}{s^{2}} $.

Further Question:

Can you suggest the reason for this source of acceleration $ a_{x} = 0.3257 \frac {m}{s^{2}} $ ?