Question

1. A crane lifts a steel submarine with a density of 8,050 kg/m3 and a mass of 25,000 kg. It is moved as a constant speed (which means the net force equals??). What is the tension in the lifting cable? The density of the water is 1030 kg/m3.

2. An Airbus A490 aircraft (which may not actually exist) is a massive plane. It has a mass of 600,000 kg and a wing area of 875 m2. The density of air is 1.35 kg/m3.

a) What pressure difference in Pascals is required to lift this aircraft?

b) If the speed of the air molecules under the wing is 80 m/s, what is the speed of the air molecules above the wing that creates this pressure difference?

c) Convert 80 m/s to mph.

Answer 1

1)

from the given data

volume of crane, V = mass/density

= 25000/8050

= 3.106 m^3

let T is the tension in the string.

as the crane is moving with constant velocity, Fnety = 0

B + T - m*g = 0 (here B is buoyant force)

T = m*g - B

= m*g - weight of the displced water by crane

= m*g - rho_water*V*g

= 25000*9.8 - 1050*3.106*9.8

= 2.13*10^5 N

2)

a) delta_P = F/A

= m*g/A

= 600000*9.8/875

= 6720 Pa

b) (1/2)*rho*(v2^2 - v1^2) = delta_P

v2^2 - v1^2 = 2*delta_P/rho

v2 = sqrt(v1^2 + 2*delta_P/rho)

= sqrt( 80^2 + 2*6720/1.35)

= 128 m/s

c) 80 m/s = 80*(60*60/1000) km/h

= 80*(60*60/1000)/1.609 miles/hour

= 179 mph