Learning Outcomes
The aim of this assessment is to help you learn to:
- Apply principles of particle kinematics and particle kinetics to simulate projectile motion.
- Apply principles of linear momentum and impact to determine the effect of impact on the velocity of a body.
- Translate equations derived from a particle dynamics analysis into a matlab program script.
The aim of this assessment is to use kinematics and kinetics relationships to analyze the motion and forces during the action of cricket bowling
Shaun Tait is one of the fastest bowlers in the world. Our aim is to use some of the fundamental particle kinematics and kinetics relationships to simulate cricket bowling.
Important parameters for this assignment
Table 1: Default parameters for kinematics and kinetics analysis of cricket bowling
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Velocity of bowler's run
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8 m/s
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Length of arm
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0.8 m
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Height of ball at release
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2.4 m
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Mass moment of inertia of the arm, I
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0.64 kgm2
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Mass of ball
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160 g
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Radius of ball
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50 mm
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Length of a cricket pitch
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20 m
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Coefficient of restitution between ball and pitch
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0.8
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Let's analyze the sequence of motions that the ball undergoes.
1. The bowler releases the ball.
The action of the bowler is to take a "run-up" towards the wicket, rotate the stretched- out arm that is holding the ball, and to release the ball at an appropriate point of that circular motion for the ball to reach the other end of the pitch as fast as it can.
(a) If a bowler takes an initial run with a velocity of 8 m/s, what is the velocity of the ball relative to the bowler before he starts the roational motion of his arm for ball release?
(b) Let us say that a bowler releases the ball after rotating the arm by 2250. As the ball is rotating about a fixed axis of rotation (around the shoulder), we can use rotational kinematics to analyze the kinematics and kinetics of the ball. Estimating the torque applied about the shoulder is 100 Nm
(i) The work done by torque for the angular displacement is very similar to the work equation for rectilinear motion. W = Tθ. The kinetic energy of a particle undergoing rotational motion KE = 0.5Iω2. I is the mass moment of inertia and is a measure of the resistance of a body to rotational motion. Using these two relationships write down the angular work-energy equation equivalent to that which was presented in class for rectangular Cartesian motion. Calculate the linear, tangential velocity of the ball when it is released by the bowler at 2250.
(ii) If you had not guessed yet from (a), the velocity we have calculated for the ball is the velocity of the ball relative to the bowler's body. With the bowler running at 8 m/s, calculate what the magnitude of the absolute velocity of the ball is. Assume that when the ball is released, the velocity vector makes an angle of 50 with the horizontal axis (see Fig. 3).
2. Projectile Motion
Use particle kinematics expressions to determine the velocity of the ball just before it hits the ground.
3. Bounce
We can simulate the path of the ball after it hits the ground using the principle of the conservation of linear momentum and the coefficient of restitution. Unlike the 1D rectilinear motion example, we are dealing with a two-dimensional coordinate system here. However, we can analyze the conservation of momentum and coefficient of restitution in each of x and y-coordinates separately to determine the velocity of the ball after impact. Calculate the velocity vector and magnitude of the ball after impact with the ground. Hints: the velocity of the ground is 0 m/s before and after impact; you can assume that the impact dominantly affects the vertical speed of the ball.
4. Towards the batsman
The ball now moves towards the batsman 20 m from the bowler's end. The height and pace of the ball can be very dangerous as AB De Villiers found in the video above. Sadly Phil Hughes died from impact of a ball to his head.
Programming
With the parameters in table 1 fixed for all simulations, write a program that will take as input (i) the applied torque about the shoulder; (ii) the angle with the horizontal axis at which the ball is released to simulate the path of the ball from the moment of release till the ball reaches the 20 m line along the pitch. Assume that the bowler always takes a 2250 rotation of the arm. When the user clicks run, the program should generate an animation of the ball movement for the two parameters that the user inputs. Hint - all the workings you have done above give you the steps you need to follow to code the program up.
- implementing a basic code that correctly predicts the dynamics of the ball for 1 bounce.
- If the angle of release is large enough the ball may bounce multiple times before reaching the batsman at the 20 meter mark.