Question

2) The UMD glider has a mass of 51kg and is neutrally bouyant at its neutral state (without any volume anomaly). It can change its effective displacement volume by approximatly ± 2x10^-4m³.

a) What is the effective upward or downward net force on the glider when it changes its displacement volume?Show you work and explain each step.

b) If the glider were designed to move vertically through the water (It's not, but reality is a lot more complicated in this case), what would its terminal velocity be ( up or down)? Assume it has a radius of .10m and a drag coefficient of 0.30. Show you work and explain each step.

Answer 1

(a) When it changes its displacement volume, then the effective upward or downward net force on the glider which will be given by -

F_net = _air V g

where, _air = density of air = 1.225 kg/m³

V = effective displacement volume = 2 x 10^-4 m³

g = acceleration due to gravity = 9.8 m/s²

then, we get

F_net = [(1.225 kg/m³) (2 x 10^-4 m³) (9.8 m/s²)]

F_net = 2.40 x 10^-3 N

(b) If the glider were designed to move vertically through the water, then its terminal velocity which would be given by -

v_terminal = 2 m g / _w C_drag A

where, m = mass of glider = 51 kg

g = acceleration due to gravity = 9.8 m/s²

_w = density of water = 1000 kg/m³

C_drag = drag coefficient = 0.3

A = cross section area of glider = 4r²

then, we get

v_ter = [2 (51 kg) (9.8 m/s²)] / [(1000 kg/m³) (0.3) 4 (3.14) (0.1 m)²]

v_ter = [(999.6 N) / (37.6 kg/m)]

v_ter = 26.5 m²/s²

v_ter = 5.14 m/s