Ok, I believe this is a solvable problem, relating to pedulum, collision, and conservation of energy problems. This is what I have so far:
Length of putter=.9144m (Do you think this measurement is sufficient or do I need to measure all the way to between the golfers shoulders?)
Mass of putter head=.45kg (Do you think I'd need to know the mass of the arms of the golfer and putter shaft too?
Height (h) putter raised for 20 deg. backswing= L-Lcos20 =.0551m
gravity= 9.8 m/s^2
PE=h*g*m
Velocity: PE + KE (top of backswing) = PE' + KE' (bottom or vertical part of the swing where impacts golf ball)
(.0551)(9.8m/s^2)(.45kg) + 0 = 0 + 1/2(.45kg)v^2
v = 1.04m/s
Impulse time between putter and golf ball= .005s
At this point, I can't figure out how to derive the amount of force the putter (swinging at 1.04m/s) will transfer to the golf ball (after impulse of .005s).
I believe I'd have to do something with the kinetic energy of the putter, impulse time, & F=m*a
Thnx
I guess it depens on how you put, if you break your wrists and keep your arms still ,then you are OK, if you are swinging at the shoulders, then you need the longer measurement.
Ultimately you are looking for the height of the putter head at max swing (assuming you use no mucles, which alas I think is an invalid assumption)
Ounce you have the height, you can calculate the energy of the club head (E=hmg) and then speed at the bottom (E=1/2mv^2)
Then you need to do a colision calcualtion to compute the amount of energy trasmited to the ball.
You will get a system of 2 eq. & 2 unknowns:
Mgolfball*Vgolfball+Mclub*Vclub=Vswing*Mclub (conservation momentum)
Mgolfball*Vgolfball^2+Mclub*Vclub^2=Vswing^2*Mclub (conservation Energy)
Onve you know the final vel of the ball or club, then you can calcualte the force as follows:
Change in vel/impulse time=Accel
Accel * Mass =Force