Question

The air around the spinning baseball in the following figure (top view) experiences a faster speed on the left than the right side and hence a smaller pressure on the left than the right. Suppose the ball is traveling forward in the x direction at 41.0 m/s and it breaks 16.0 cm to the left in the -y direction (neglect the pull of gravity in the z direction). Assume the ball has a mass of 142 g and a radius of 3.55 cm. In addition, assume it travels at a constant speed of 41 m/s in the xdirection from the pitcher's mound to home plate (60.5 ft = 18.44 m). Hint: The pressure difference equals the leftward force divided by the cross-sectional area of the ball, πr².

Left side x = 18.44 m Right side

1)

Determine the pressure difference between the right and left sides of the ball. (Express your answer to three significant figures.)

Answer 1

t = x / v = 18.44 / 41 = 0.449 s

s = u t + 1/2 a t²

0.16 = 0 + (1/2 * a * 0.449²)

a = 1.58 m/s²

F = m a = 142 * 10^-3 * 1.58 = 0.225 N

P = F / A = 0.225 / (pi * 0.0355²)

pressure difference = 56.8 N/m²