Question

n Chapter 5 we look at drag due to air resistance for falling objects. Using the Dv form of dr discussed in class, write a program (or solve analytically) to determine how long (sec.) and how far m) a 150 gram ball whose radius is 3.5cm would fall before it reached 75% of its terminal velocity. Assume ball falls in air whose density is 1.21 kg/m3, has a drag coefficient C .3, cross-sectional area s just the disk a sphere presents to the eye. Due Tues. 2/19. Hand in printout of program and nswers. Your answer should be good to 1%. (How will you know?) Recall from class D ½ рАС

Answer 1

The force acting on the ball at any point F = mg - Du^2 ma = mg - Dv^2 m d v/dt = mg - Dv^2 at terminal velocity dv/dt = 0 mg = D v^2 v_T = squareroot mg_D dt = m/mg - D v^2 dv dt = m/D [1/mg/D - v^2 dv] integral dt = m/D integral dv/mg/D - v^2 Now, integral dx /aa^2 - x^2 = 1 /2a log Vertical-bar a + x/a - lambda Vertical-bar + c \r\n t = m/D times 1/ 2 squareroot mg/D log Vertical-bar squareroot g/D + g/squareroot g/D + v Vertical-bar + c t = m/2 squareroot mg D log Vertical-bar squareroot g/D + v/squareroot g/D - v Vertical-bar + c at t = 0 v = 0