Question

Lecture 2 Examples: Density, Pressure and Buoyancy During the Great Mississippi Flood of 1993, the level in St. Louis tended to rupture first at the bottom. Why? You are asked to bring a cylindrical iron rod of length 85.8cmand diameter 2.85cm from a storage room to a machinist. Will you need a car? What is the average density of the sun? What is the average density of a neutron star that has the same mass as the Sun but a radius of only 20km? Black smokers are hot volcanic vents that emit smoke deep in the ocean floor. Many of them teem with exotic creatures, and some biologists think that life may have begun around such vents. The vents range in depth from about 1500m to 3200m below the surface. What is the gauge e pressure at a3200m deep vent, assuming that the density of water dees not vary, Express your answer in pascals and in atmosphere. A bareel contains a 0.120-m layer of oil floating on water interface? What is gauge pressure at the bottom of the barrel? The human eardrum (typical diameter 8.2mm) can withstand forces up 1 5-N above the force from atmospheric pressure without damage. When you go scuba diving in the ocean, below what depth could damage to your eardrum start t0 occur. An ore sample weights 17.50N in air. When the sample is suspended by a light core and totally impressed in water, the tension in the core is 11.20N. Find the volume and density of the sample. A rock is suspended by a light string. When the rock is in air, the tension in the string is 39.2N. When the rock is totally immersed in water, the tension is 28.4N. When the rock is totally immersed in an unknown liquid, the tension is I8.6N. What is the density of the unknown liquid?

Answer 1

1)Because the pressure is the highest at the bottom and probably the thickness of the levee was independent of depth.

2)Mass=rho*pi*r^2*h=7870*pi*0.01425^2*0.858=4.31 kg.

Clearly a cart is not needed.

3)Density of sun=mass/volume=1.99*10^30/(4.3*pi*(6.96*10^8)^3)=436.93kg/m^3

4)Gauge pressure=rho*g*h=1000*9.81*3200Pa=3.139*10^7Pa=309.8 atm

5)Gauge pressure at interface=rho1*g*h1=600*9.81*0.12=706.3Pa

Gauge pressure at bottom=rho1*g*h1+rho2*g*h2=600*9.81*0.12+1000*9.81*0.25=3158.8Pa

6)Pressure=F/A=1.5/(pi*0.0041^2)=28404Pa

h=P/rho*g=28404/(1000*9.81)=2.90m

7)Buoyancy=17.5-11.2=6.3N

Volume of water=buoyant force/(rho*g)=6.3/(1000*9.8)=6.43*10^-4m^3

Density=Mass/volume=(weight/g)/(volume)=(17.5/9.81*6.43*10^-4)=2774kg/m^3

8)Buoyant force=39.2-28.4=10.8N

Volume=10.8/(9.81*1000)=1.101*10^-3m^3

Buoyant force in other liquid=39.2-18.6=20.6N

Density=buoyant force/(g*volume)=20.6/(9.81*1.101*10^-3)=1907kg/m^3