L6 - Oblique impacts

Question 1

Newtonian Impacts

Sketch a diagram of the ‘Rigid ball Rigid surface’ model

Define the nomacleture

o at contact - ball has vertical reaction, __( when vy is __) & frictional force ,F (inducing top spin)

o Top spin defined as ___ as are the velocities

Answer 1

R, -ve

+ve

Question 2

_Newtonian Impacts _

What are the 2 cases of newtonian oblique impacts?

Answer 2

 Ball slides throughout impact

 Ball rolls throughout the impact

Question 3

Newtonian Impacts

What are the assumptions when using newtonian impacts modelling ? (4 assumptions) :

what is an advantage and a disadvantage of using this method ?

Answer 3

 Constant coefficient of friction μ

 Constant coefficient of restitution ,e

 Either slipping or rolling

 No deformation (ball or surface)

o These equations can make close predictions

oRarely valid in sport

Question 4

Simple predictions (using Newtonian principles) #1

For the horizontal velocity (ms^-1) after impact, what are the equations if:

the ball is slipping ?

the ball is rolling?

Answer 4

Question 5

Simple predictions (using Newtonian principles) #2

For the vertical velocity (ms^-1) after impact, what are the equations if:

the ball is slipping ?

the ball is rolling?

Answer 5

Question 6

Simple predictions (using Newtonian principles) #3

For the rebound spin (Rad s^-1) after impact, what are the equations if:

the ball is slipping ?

the ball is rolling?

Answer 6

Question 7

The boundary between slipping and rolling

It is evident that the transition between slipping and rolling occurs with ______ _______ such that the horizontal rebound velocity vx_f for slipping is equal to that for rolling, i.e.

(define the equation)

This gives the condition for rolling to occur as:

(define the equation)

Answer 7

inbound conditions

Question 8

Impacts on surfaces – other methods of modelling

Newtonian models go a long way to understand the performance of sports balls during impact with a surface, but they can be limited in certain situations, due to the following assumptions ( 4 assumptions):

Answer 8

• The ball and the surface are treated as rigid (no deformation)
• If slipping, F=µR throughout impact
• Otherwise, the ball simply rolls off the surface (no ‘over-slip’)
• Impulsive forces are ignored (e.g. the effect of mass coming to rest on the surface).

Question 9

Impacts on surfaces – other methods of modelling

sketch a diagram of the mass spring damper model

Answer 9

Question 10

Impacts on surfaces – other methods of modelling

Sketch a diagram of impulsive force modelling

Answer 10

Question 11

Impacts on surfaces – other methods of modelling

Name 2 other methods of oblique impact modelling :

How do you choose which model you use ?

Answer 11

• Empirical modelling
• Finite-element modelling

These methods all have their advantages and disadvantages and each impact problem has to be treated individually.