(a) Show that the pressure exerted by a fluid P (in pascals) is given by P = hdg, where h is the column of the fluid in metres, d is the density in kg/m-3, and g is the acceleration due to gravity (9.81 m/s2). (Hint: See Appendix 2.). (b) The volume of an air bubble that starts at the bottom of a lake at 5.24C increases by a factor of 6 as it rises to the surface of water where the temperature is 18.73C and the air pressure is 0.973 atm. The density of the lake water is 1.02 g/cm3. Use the equation in (a) to determine the depth of the lake in metres.

B) THE DEPTH OF THE LAKE IS 0.060 m

Explanation:

b) Determine the depth of the lake in metres

1. Using the general gas law, we will calculate the initial pressure of the air bubbles.

P1V1 /T1 = P2V2/T2

P1 = Unknown

T1 = 5.24 °C

T2 = 18.73 °C

P2 = 0.973 atm

V1 = V1

V2 = 6V1

P1 = P2 V2 T1 / V1 T2

P1 = 0.973 * 6V1 * 5.24 / V1 * 18.73

P1 = 5.09852 * 6 / 18.73

P1 = 30.59112 / 18.73

P1 = 1.633 atm.

2. Calculate the depth of the lake:

             Pressure = length * density * acceleration

            length = Pressure / density * acceleration

Pressure = 1.633 atm = 1.633 * 101, 325 Nm^2 = 165, 463.725 Nm^2

Density =  1.02 g/cm3 = 1.02 * 10^3 kg/m^3

Acceleration = 9.8 m/s^2

So therefore, the length in metres is:

Length = density * acceleration / pressure

Length =  1.02 *10^3 * 9.8 / 165, 463.725  

Length = 9.996 * 10^3 / 165 463.725

Length = 0.06 m

Hence, the depth of the lake is 0.06 m

first let us lay out the formula for potential

and kinetic energy:

pe = mgh

ke = (mv^2)/2

where: m=mass, v=velocity, g=gravitational

acceleration, h=height

calculating for mass using the known values of

pe:

340j = m (9.81 m/s^2) (50ft) (1m/3.28ft)

m = 2.27 kg

the law of conservation of energy states that

energy is neither created nor destroyed. therefore, the change in kinetic

energy from 50 ft to 35 ft would be equal to the change in potential energy

from 50 ft to 35 ft. however it would be opposite in signs since one is losing

while other is gaining.

ke(35ft) – ke(50ft) = - [ pe(35ft) – pe(50ft]

ke(50ft) = 0 since the brick is initially at rest

ke(35ft) = 340j - 2.27kg (9.81 m/s^2) (35ft)

(1m/3.28 ft)

ke(35ft)

= 102.38 j

i just learnt this recently but i need to look through my notes again