To home late 7.) A pitcher throws a basball towards hose plate with speed -42m/s

Question

To home late 7.) A pitcher throws a basball towards hose plate with speed -42m/s 42 m/s constant). The pitcher also spins the baseball so that it rotates at ?-742 rpen (nmumedconstant) in clockwise direction. The radius of the baseball isr23em and the massism 148 g a) What is the momentary speed of the left (L) and right (R) side of the baseball? 742 rpm b) The momentary speed of the ball determines the speed of air ow near the surface of the ball Find the pressure difference between the left and right side of the ball. Use ? = 1.29 kg/m" for the density of air.

Explanation / Answer

7. given speed of baseball v = 42 m/s

angular speed, w = 742 rpm, clockwise direction

r = 2.3 cm

m = 148 g

a. momentarily speed on the left and right side of the base ball is

Vl = v + w*r = 42 + 742*2*pi*2.3*10^-2/60 = 43.78714734 m/s

Vr = v - wr = 42 - 742*2*pi*2.3*10^-2/60 = 40.21285 m/s

b. pressure on the left side of the ball = Pl

pressure on the right side of the ball = Pr

pressure difference = dP = |Pl - Pr|

now, from berboullis theorem

dP = 0.5*rho*(Vl^2 - Vr^2)

rho = density of air = 1.125 kg/m^3

hence

dP = 168.885423669 Pa

c. D = 18.4 m

as Vl > Vr

the ball moves to the suction surface, i.e left

towards -ve x axis

total deflection = x

force on ball to the left = dP*pi*r^2

acceleration , a = force/m

x = 0.5*a*t^2

t = D/v

hence

x = 0.5*(dP*pi*r^2/m)*(D/v)^2

x = 0.5*(168.885423669*pi*0.023^2/0.148)*(18.4/42)^2

x = 0.1819881062092 m

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