A baseball of mass and radius is thrown at and travels to the batter

PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Fluids & Continuum Physics · Kinematics and Newtonian dynamics of particles

Fluids and Continuum Physics, Ch Bernoulli at work: Venturi meters, Pitot tubes and lift

Problem

A baseball of mass

0.145\ \mathrm{kg}

and radius

37.0\ \mathrm{mm}

is thrown at

38.0\ \mathrm{m\,s^{-1}}

and travels

18.4\ \mathrm{m}

to the batter. It spins about a vertical axis: seen by the pitcher looking down the line of flight, the surface on the right-hand side of the ball is moving forwards, towards the batter, and the surface on the left-hand side is moving backwards. The air has density

1.20\ \mathrm{kg\,m^{-3}}

. Model the sideways (Magnus) force as

F = \tfrac12\rho U^2(\pi r^2)C_L

with

C_L = 0.20

for this spin rate, acting horizontally and perpendicular to the line of flight, constant over the flight. Ignore drag, so the forward speed stays at

38.0\ \mathrm{m\,s^{-1}}

. ((a)) Does the ball break to the pitcher's left or to the pitcher's right? Justify it from the air speeds and pressures on the two sides. ((b)) Find the magnitude of the sideways force and the sideways acceleration. ((c)) Estimate the sideways deflection at the batter, measured from the straight path a spinless ball would have followed.

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