Question

(50 points) (Q2.9 in the textbook) A baseball (radius 0.0366 m, mass 0.0145 kg at the top of the Empire State Building (height 1250 ft). Calculate (a) the initial potential energy of the baseball, (b) its final kinetic energy, and (c) the total energy dissipated by the falling baseball by computing the line integral of the force of air resistance along the baseball's total distance of fall. Compare this last result to the difference between the baseball's initial potential energy and its final kinetic energy. (hints: In part (c) make approximations when evaluating the hyperbolic functions obtained in carry out the line integral.)

Physics: Analytical Physics

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Answer 1

By the given Data. Consider a base ball radius = 0.0366m mass = 0.0145kg. Building height = 1250ft consider a baseball is dropped from the empire state building. Calculate the initial potential energy of the ball. v_1 = mgh There, v_1 is the initial potential energy of the ball. 'm' is the mass of the ball. 'g' is the accerlation due to gravity 'h' is the height at which the ball is dropped from the ground \r\n Substitute the m, g, h values in the equation v_1 = mgh v_1 = 0.0145 times 9.81 m/s^2 times (1250ft times 0.03048 m/ft) v_1 = 0.0145 times 9.81 times 381 v_1 = 0.0145 times 9.81 times 381 = 0.142245 times 381 = 541.95345J v_1 = 541.95345J Initial potential energy of the baseball is v_1 = 541.95345J (b) Calculate the air drag co-efficient for the ball. c = 0.22D^2 c = 0.22 times (2r)^2 c = 0.88r^2 \r\n There 'c' is the air drag co-efficient for the ball.