Physics in the world of cricket

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1. Physics in the world of cricket Projectile motion momentum magnus effect numericals

2. CRICKET BALL : A PROJECTILE PROJECTILE Projectile is the name given to a body thrown with some initial velocity, and then allowed to move in two dimensions under the action of gravity alone, without being propelled by any engine or fuel. The path followed by a projectile is called its trajectory.

3. Examples of projectiles A cricket ball hit by a bat. A javelin or hammer thrown by an athlete. A bullet fired from a rifle. A piece of stone thrown in any direction.

4. ASSUMPTIONS IN PROJECTILE MOTION 1. There is no frictional resistance of air. 2. The effect due to rotation of earth and curvature of the earth is negligible. 3.The acceleration due to gravity is constant in magnitude and direction at all points of the motion of projectile.

5. Maximum Horizontal Range. we note that for a given speed u of the object, the value of horizontal range depends upon angle of projection as g is constant at a place. Therefore horizontal range R will be maximum if Sin 2 θ = maximum = 1 = sin 90° Or 2 θ =90° or θ =45°

6. HEAVY OR LIGHT BAT Law of conservation of momentum  Momentum is total quantity of motion possessed by body It is product of mass and velocity If the Bat is heavy, then even a slight swing can provide enough momentum to ball to cross the boundary. Whereas if bat is light it can swing 10% faster and impart same momentum to ball. Having a heavy bat gives more advantage as it proves to be more powerful. If all bats are swung at same medium speed. Heavy & light terms are relative with respect to age. Therefore one must use a bat as heavy as one feels comfortable to swing.

7. Why a cricketer lowers his hands while catching a ball ? Impulse It is effect of force acting for a short interval of time. According to Newton’s 2 nd law Rate of change of momentum = Force applied. If time period dt is increased than Impact force decreases.

8. Why a cricketer lowers his hands while catching a ball If suppose a 0.16 kg cricket ball hits a bat at 100 km/ hr and then comes off the bat at 100 km/ hr in 0.001 sec. The average force on ball is 8800 N which is enough to lift 880 kg of mass off the ground. That is why it hurts to get struck by ball. Therefore while catching cricketer lowers his hands to increase time interval of change in momentum thereby impact force reduces.

9. SPIN 1. The first axis is vertical pointing towards sky. 2. A ball that spins about vertical axis will deflect in air to left or right and there is no deflection when it bounces.

10. SPIN The second axis points along the pitch towards the batsman when cricket ball spins or about this axis. It does not deflect in air, but deflects sharply towards left or right after the bounce. By dropping the spinning ball vertically we can notice this change.

11. The third axis is across or perpendicular to pitch. Spinning the ball about third axis results in top spin or back spin. A Top spin ball dives towards the pitch faster and bounces at reduced angle since it kicks forward when it bounces. A back spin ball kicks up after it bounces, causing the ball to slow down. The actual result depends on both the amount of spin and angle of incidence. SPIN

12. Swing Ball surface If during the play one side of the ball roughs up and other side remains smooth. Then swing occurs Swing is swerving of cricket ball towards left or right as it moves through air. This happens when ball spins about its vertical axis or because it spins about an axis perpendicular to the seam.

13. Swing The fast bowlers swing the ball by making the seam inclined at angle of 15° to 25° to the direction that the ball is headed such that the smooth portion of ball is above & in front. In this way the air flows smoothly around the smooth half but it becomes turbulent on other side as it has to flow past the seam.

14. swing The turbulent air is at higher velocity. Therefore according to Bernoulli’s theorem the pressure on these side (rough) decreases than on smooth flowing air therefore the ball gets pushed sideways. This is also the Magnus effect. This sideway swing force is maximum when speed of ball is around 100 km/hr. But it speed of ball increases. The reverse swing occurs because the flow of air over smooth surface becomes turbulent. The effect can occur at low speeds if rough end side is put forward.

15. Swing Other factors : affecting swing are the atmospheric pressure : - Due to evaporation of ground moisture. The water vapor content of air over pitch increases. This increases the partial pressure and thereby air pressure therefore as match progress the fast bowlers will be able to get more swing if they manage roughness/shine factor well.

16. Outswing and inswing   (1) Holding the ball for an out swinger with shiny/wet side on right side The ball initially moves out in the air and comes back to the batsman sharply. Usually, a batsman can be out by leg before as the tends to play along wrong line.

17. Outswing and inswing (2) Holding the ball for an in swinger, with shiny side on the left side The ball initially moves towards the batsman and at last moment darts away from the batsman. A batsman can be caught behind the wickets and sometimes bowled.

18. Shining the Ball Most of us have watched cricketers rub the ball near their crotch almost every time they have the ball. The question is why? Shining the ball helps the ball to swing. As the game goes on the ball receives consistent impact on the surface. But one side of ball is emphasized and taken care of by the bowlers. What you should end up with is ball distinctly shiny on one side and rough on other. If projected, a bowler can chose which direction he wants the ball to swing. If rough side is on left side the ball will swing towards left and if it is on right side it will swing towards right. Aerodynamics, Bernoulli theorem explains why ball swings.

19. STREAMLINE AND TURBULENT FLOW Streamline flow of a liquid is that flow in which every particle of the liquid follows exactly the path of its preceding particle and has the same velocity in magnitude and direction as that of its preceding particle while crossing through that point. Turbulent flow When a liquid moves with a velocity greater than its critical velocity, the motion the particles of liquid becomes disorderly or irregular. Such a flow is called turbulent flow.

20. Curved motion of spinning ball (Magnus effect) When a spinning ball is thrown, it deviates from its usual path in flight. This is due to magnus effect.. If the ball is spinning as well as moving linearly, the streamlines at the top of ball due to two types of motion are opposed to each other and those below are in the same direction. As a result of it, the velocity of air flow is greater below than above the ball. Now, according to Bernoulli’s principle, the pressure on the upper side of the ball becomes more than the pressure on the lower side of ball. Due to it, a resultant force F acts upon the ball at right angle to the linear motion in the downward direction, resulting the ball to move along a curved path. This dynamic force due to spinning of ball is called Magnus effect .

21. Six or Four? S2) Sachin Tendulkar, the little master is batting at the crease. Glenn Mc Grath , delivers a short–pitched ball and Tendulkar pulls it. The boundary is unguarded. Tendulkar strikes the ball at an angle of projection of 15° with a velocity of 35m/s. Decide whether the ball will cross the boundary for a sixer or it will fetch only a four.

22. 1Sol : Initial Velocity of the ball, u = 10 m/s. Retardation of the ball due to friction, a = 1.25 m/s 2 Radius of the circular field = 50m Final velocity oif the ball v = 0, as it come to rest due to retardation. Now, we have to find whether the ball crossed the boundary or no. The formula connected with u, v, a and S is v 2 – u 2 = 2aS 0 – (10)2 = 2 × (1.25) ×S But the radius of the field is 50m, and the ball is stopped at a distance of 40m. Therefore the boundary is saved and Australia will not get the boundary.