L4 - Impacts with distributed masses Flashcards
How are a ball and bat simplified for modelling?
Ball – point mass
Bat – distributed mass of infinite stiffness
As the bat is a distributed mass, energy will go into both its’ rotation and translation.
Draw a diagram of the movements experienced by a ball and bat after an impact.
Tada
Give 5 limiting assumptions of rigid body modelling
- Perfect technique (In this case, contact force is horizontal)
- 2D model
- e (coefficient of restitution) is independent of velocity
- e incorporates all losses in ball
- grip has no effect on resultant ball velocity (would depend on dimensions of bat and contact time of ball)
How could you increase the accuracy of rigid body modelling
Modifying the model such that e incorporates losses in the bat due to non-infinite stiffness
If the depicted equation describes the starting point, describe with words, the method for calculating the velocity of the ball
- Apply coefficient of restitution
- Apply conservation of linear momentum
- Apply conservation of angular momentum
- Rearrange
- Simplify through assuming z=0 (impact takes place on centre of mass)
From the same starting point, as depicted, calculate the resultant velocity of the ball using the previously described method in terms of:
mass of racket M, velocity of racket V, coefficient of restitution e, initial velocity of the ball vb and mass of the ball mb
HEY! WHATS GOING ON HERE?
Timon (1994)
What is the term Centre of Percussion used for in the sports equipment design field?
Rigid racket, held at H, directional blow received at COP (distance x from COM).
COP is a recognised term describing sweet spot locations.
The Sweet Spot and the instantaneous centre of rotation:
If impact occurs away from ___ it results in ___________ of COM and rotation of body ______ ___, causing a reactive _____ at the hand (_______ effect).
As these movements occur simultaneously, there will exist a point for which the resultant movement is 0. This _________________________ describes this point.
When ____ at this centre, the jarring effect is _ if the impact was _________.
If impact occurs away from COM it results in translation of COM and rotation of body around COM, causing a reactive force at the hand (jarring effect).
As these movements occur simultaneously, there will exist a point for which the resultant movement is 0. This instantaneous centre of rotation describes this point.
When held at this centre, the jarring effect is 0 if the impact was at the COP.
Name the assumption introduced so that factors associated with the COP can be calculated.
Name a possible modelling situation for which this method subsequently cannot apply
The impact force producing the resultant linear and rotational movement is a constant force acting for time t.
Viscoelastic impacts
How could the COP be better described to increase accuracy?
What variables would be needed for its application?
Due to infinite stiffness assumption, COP is displaced from theoretical solution and would be better described as a migratory locus
(dependant of racket stiffness and motion of hand during impact).
Method for finding x if b is known:
F=MA gives rise to a ______ around the ___, which produces a clockwise _______ ______ around the COM.
alpha =
I is about an axis through the COG perpendicular to the diagram below.
There will be a point on the ________ ____ of the COM to the impact, where _ and _ cancel each other out causing the resultant motion to be _.
as alphabeta = and F/M =
then x =
F=MA gives rise to a torque around the COG, which produces a clockwise angular acceleration around the COM.
(EQN 1 in picture)
I is about an axis through the COG perpendicular to the plane of that diagram.
There will be a point on the opposing side of the COM to the impact, where A and cancel each other out causing the resultant motion to be 0.
(EQN 2 in picture)
