Physics of Ball Catching

When the ball arrives down it has both kinetic energy due to the motion and potential energy due to the height. When one tries to catch the ball, the total energy should be dissipated by the hands clasped together. So when does the ball stick and when does it fall out?

Let us get into some more details when a ball is hit by a batsman. The ball travels upwards until the velocity becomes totally zero. There is also the case where the may be a sufficient horizontal component of the velocity which would make the ball fly out of the stadium. The mechanics equations described below will consider those cases where the ball falls down inside the stadium.. So after the velocity becomes zero, the ball falls down again due to the force of gravity.

Let us now discuss the mechanics of the arm and the effect of the contraction of the muscles on the arm. The arm has a motion that neutralizes the motion of the ball by retracting in the opposite direction of travel of the ball. Also the inner hands which hold the ball have restitution and friction. Studies show that the tensile stress in the upper limb can go up to 600 Newtons.

Let us apply the law of conservation of energy to a ball that is reached the height h and is descending downwards. After that let us substitute some numbers.

0.5 * m * v * v = m * g * h (Law of Conservation of Energy)

v* v = 2 * g * h

v = sqrt(2*g*h)

So the total energy possessed by the ball when travelling downwards is simply 0.5 * m * v * v or mgh.

Let us calculate the energy of the ball in downward motion at different heights.

0.15 * 9.81 * 1 = 0.l4N at 1 metre max height, at 100 metre max height the energy possessed by the ball 0.15 * 9.81 * 100 = 147 Newtons.

In order for the energy on the ball to be more than the Tensile stress induced in the arm/hands the maximum height reached by the ball should be 0.15 * 9.81 * h = 600 or h = 400 metres.

For the ball to reach a 400 metre height, the speed at which it must be hit is approximately sqrt( 2 * g * h) = 85 m/s or 340 km/hour.

So appears as though the arms and the muscles are well equipped to hold catches from normal cricket shots. The second aspect of catching is the reason why the ball sticks when the gloves are worn is that the surface area exerts a reaction force in the form of friction and restitution. Our hands are much softer than gloves and so offer lesser frictional force and an outward force due to restitution.

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