05-12-2012, 05:29 PM
Maths Of Sports
Maths Of Sports.ppt (Size: 114 KB / Downloads: 96)
The Movement of a Ball over a plane Surface
Consider a ball of mass M and radius a.
Let coefficient of Sliding friction be µ
Then friction on Ball – F= µMg (1)
This force will have 2 consequences
Linear deceleration of ball
moment of force about C (centre) will produce a clockwise angular acceleration
Impact Times
In most games, experiments indicate that the linear compression x of a golf ball is related to the applied force F by a law of the form of F=Kx
This leads to a relation between impact times and velocity, As velocity increases, the duration of impact decrease, approaching a constant value at higher velocities.
Energy loss and efficieny
in golf, some of the energy loss will be dissipated as heat, energy converted into heat = 0.5MV² - 0.5MV´² - 0.5MV´²
= mMV²(1-e²)/2(m+M) = (0.047)(0.20)(50²)(1-0.49)/2(0.246) = 23 joules
Assuming a specific heat capacity of rubbe about 1700joulekg^-1k^-1, this suggests a rise in tempreture of ball during impact ≈ 0.3°K