Question

1.

a. Two equal sized and shaped spheres are dropped from a tall building. Sphere 1 is hollow and has a mass of 1.0 kg. Sphere 2 is filled with lead and has a mass of 9.0 kg. If the terminal speed of Sphere 1 is 6.0 m/s, the terminal speed of Sphere 2 will be

b.The cross sectional area of Sphere 2 is increased to 3 times the cross sectional area of Sphere 1. The masses remain 1.0 kg and 9.0 kg, The terminal speed (in m/s) of Sphere 2 will now be

2.

A man weighs 180 lbs at the surface of the Earth. The radius of the Earth is 4,000 mi. The man’s weight at a distance 4,000 mi above the Earth is

Answer 1

$1.\:Part\:a:$

$Terminal\:speed\:is\:defined\:as:$

$v_{T}^{2}=\frac{2mg}{D\rho A}$

$where$

$m=mass\:of\:object$

$g=gravity$

$D=object\:drag\:coefficient$

$\rho =density\:of\:medium$

$A=object\:area$

$For\:sphere\:1:$

$D=\frac{2mg}{v_{T}^{2}\rho A}=\frac{2\left ( 1\:kg \right )\left ( 9.8\:\frac{m}{s^{2}} \right )}{\left ( 6\:\frac{m}{s} \right )^{2}\rho A}=\frac{0.54}{\rho A}\:\frac{kg}{m}$

$terminal\:speed\:of\:sphere\:2:$

$v_{T}=\sqrt{\frac{2\left ( 9\:kg \right )\left ( 9.8\:\frac{m}{s^{2}} \right )}{\left ( \frac{0.54}{\rho A} \:\frac{kg}{m}\right )\rho A}}={\color{Blue} 18.09\:\frac{m}{s}}$

$Part\:B:$

$A_2=3A_1$

$v_{T}=\sqrt{\frac{2\left ( 9\:kg \right )\left ( 9.8\:\frac{m}{s^{2}} \right )}{\left ( \frac{0.54}{\rho A_1} \:\frac{kg}{m}\right )\rho 3A_1}}={\color{Blue} 10.43\:\frac{m}{s}}$