Tennis Kinematics Transient Analysis: A Ball Spin & Racket Collision Description by Miltiadis A. Boboulos - HTML preview

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² cos²α+² sin²
λ α (Eq. 4b) and the relation between the angle of incidence α and the angle of reflection β: tg β − λ

 

⁼ . (Eq. 4c) _{tg α k}

 

a) Experimental determination of the restitution coefficient

The restitution coefficient k can be determined in several ways. But the easiest way to determine it is to use the theorem for the kinetic energy variation to derive u and v [21]:

E_k1− E_k0= A₀₁, (Eq. 5) Where E_k1 and E_k0 are the kinetic energies at the end and at the beginning of the process being observed and A₀₁ is the work performed for this period of time. Applying this theorem we get the following values for these speeds:

u= 2gh₁ and v= 2gh₀ . Then, according to the coefficient of restitution formula we get the following expression:

 

k =^{u h1}_{. v h0}

 

b) Kinetic energy loss during material particle impact

The kinetic energy loss resulting from the collision phen omenon is essential to be determined as this can be used to judge the characteristics of the ball-tennis racket system. To determine this we assume that a momentary perfect but imperfectly elastic contact is available at the point, i.e. 0<k<1 and λ = 0. As a result of mathematical transformations we can top the following expression for the value required [21]:

Δ

 

E
k

 

=
−