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Question: Important parameters for this assignment Table 1: Default parameters for kinematics and kinetics ...

Important parameters for this assignment

Table 1: Default parameters for kinematics and kinetics analysis of cricket bowling

Velocity of bowler’s run = 8 m/s

Length of arm = 0.8 m

Height of ball at release = 2.4 m

Mass moment of inertia of the arm, I = 0.64 kgm^2

Length of a cricket pitch = 20 m

Coefficient of restitution between ball and pitch = 0.8

Question 1. By considering work and energy conservation (not covered in this unit), we arrive at the following equation that relates torque (T [Nm]), angular displacement (? [rad]), the mass moment of inertia of the arm (I [kg m2]), and angular velocity (? [rad/s]): ???? = 1/2* ????^2 Use the above expression to calculate the linear tangential velocity of the ball, v [m/s] when it is released by the bowler after a rotation of 225°, with an estimated torque applied to the shoulder of 100 Nm (Figure 1). (1 mark)

Question2. The linear tangential velocity of the ball, v you have calculated in Question 1 is relative to the bowler. Furthermore, it is directed an angle, ? of 5° below the horizontal (see Figure 3). Given that the bowler was running at a horizontal velocity (vbowler) of 8 m/s during the release, use your knowledge of vector arithmetic to calculate:

(a) The absolute velocity vector of the ball after release.

(b) The magnitude of the ball’s absolute velocity after release.

After being released, the ball will follow a defined trajectory as it falls to the ground under the influence of gravity.

Question 3 Use your knowledge of particle kinematics to determine:

(a) The velocity vector of the ball just before it hits the ground.

(b) The magnitude of the ball’s velocity just before it hits the ground.

The ball will bounce after it hits the ground. We can simulate the trajectory of this bounce using the principle of conservation of linear momentum and the coefficient of restitution. Unlike the 1D rectilinear motion example covered in lectures however, we are dealing with a 2D coordinate system here. Thus, we will need to perform our analysis in each of the x and y-coordinates separately to determine the velocity of the ball after impact with the ground.

Question 4. By considering conservation of momentum and the coefficient of restitution, calculate: (a) The velocity vector of the ball after impact with the ground.

(b) The magnitude of the ball’s velocity after impact with the ground.

Hint: The velocity of the ground remains 0 [m/s] before and after impact, and you may assume that the impact dominantly affects the vertical speed of the ball.

Answer 1

1. We assume rotation bowler's hand starts from rest.

The angular accleration of bowler's hand is given by

The angular velocity of arm after rotation of 225⁰ is

Or

Hence linear tangential velocity of the ball after release with respect to bowler is

2. a) Refer the diagram below:

Absolute velocity of ball with respect to ground is given by

b) The absolute velocity of ball is given by

3. a) Neglecting air resistance, the horizontal velocity of ball remains constant

The vertical velocity is given by

Or

Hence ball velocity just before impact is

b) We denote 1 as condition before impact and 2 as condition after impact.

The magnitude of ball velcocity just before impact is

4. a) Since the pitch is horizontal, there is no change of ball velocity in horizontal direction due to impact.

With coefficient of restitution between ball and pitch as e=0.8 and pitch velocity after impact as 0

Or

This velocity is vertically up as ball changes direction in y direction after impact.

Hence

b) The magnitude of ball velocity after impact is