phy 231 1 physics 231 lecture 22: pressure remco zegers walk-in hour: thursday 11:30-13:30 am...
Post on 21-Dec-2015
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TRANSCRIPT
PHY 2312
Previously
Solids: LA
FL
LL
AFY
0
0/
/ Young’s modulus
xA
Fh
hx
AFS
/
/Shear modulus
pressureP
VV
P
VV
AFB
00 //
/ Bulk modulusAlso fluids
P=F/A (N/m2=Pa)
=M/V (kg/m3)
General:
PHY 2313
Force and pressure
A P=0Vacuum
Air (P=1.0E+5 Pa)
F
Force due to pressure difference: Fpressure=PAIf A=0.01 m2 (about 10 by 10 cm) thena force F=(1.0E+5)*0.01=1000N is needed to pullthe lit.
What is the force needed to move the lit?
PHY 2315
Pressure vs Depth
Horizontal direction:P1=F1/A P2=F2/A F1=F2 (no net force)So, P1=P2
Vertical direction:Ftop=PatmAFbottom=PbottomA-Mg=PbottomA-gAh
Since the column of water is not moving:Ftop-Fbottom=0PatmA=PbottomA-gAhPbottom=Patm+ gh
PHY 2316
Pressure and Depth:
Pdepth=h =Pdepth=0+ gh
Where:Pdepth=h: the pressure at depth hPdepth=0: the pressure at depth 0=density of the liquidg=9.81 m/s2
h=depthPdepth=0=Patmospheric=1.013x105 Pa = 1 atm =760 TorrPascal’s principle: If P0 changes then the pressures at all depths changes with the same value.
PHY 2317
A submarine
A submarine is built in such a way that it can stand pressuresof up to 3x106 Pa (approx 30 times the atmospheric pressure). How deep can it go?
Pdepth=h =Pdepth=0+ gh3E+06=(1.0E+05)+(1.0E+03)(9.81)hh=296 m.
PHY 2319
Your homemade pressure difference meter (PART I)
Pdepth=h =Pdepth=0+ gh
Part 2 on Friday!
h1
h2
PHY 23110
Pascal’s principle
In other words then before: a change in pressure applied to a fluid that is enclosed in transmitted to the wholefluid and all the walls of the container that hold the fluid.
P=F1/A1=F2/A2
If A2>>A1 thenF2>>F1.
So, if we apply a smallforce F1, we can exerta very large Force F2.
Hydraulic press demo
PHY 23111
Hydraulic brake
6.4cm2 1.8 cm2
F=44N
R=0.34 mcoef offriction: 0.5
What is the frictionaltorque about the axle exerted by the shoe on the wheel drum when a force of 44N is applied to the pedal?
FMC/AMC=FBC/ABC
FBC=44*1.8/6.4=12.4 NFshoe-drum=Fdrum-shoe=normal forceFfriction=N=0.5*12.4=6.2N
=F*R=6.2*0.34=2.1 NM
n
F
PHY 23112
Pressure measurement.
The open-tube manometer.The pressure at A and B isthe same:P=P0+ghso h=(P-P0)/(g)
If the pressure P=1.01 atm, what is h? (the liquid is water)h=(1.01-1)*(1.0E+05)/(1.0E+03*9.81)= =0.1 m
PHY 23113
Pressure Measurement: the mercury barometer
P0= mercurygh
mercury=13.6E+03 kg/m3
mercury,specific=13.6
PHY 23114
Pressure at different altitudes
The pressure in the lecture room equals 1 atm (1.013E+05 Pa). What will the pressure on the 6th floorof the BPS building be (h=20m)? And at the top ofmount Everest (h=8500 m)?
Just like the case for a fluid, the pressure changeswith depth (height in the case of air).Plecture room=P6th floor+ airghP6th floor=Plecture room-airgh=1.013E+05-1.29*9.81*20=
=1.010+05 Pa ( 3 promille change)Pmount everest=1.013E+05-1.29*9.81*8500=-6.3E+03 Pa????The density of air changes with altitude, and so the equation does not hold; it is very easy to compress air(small bulk modulus) compared to e.g. water.(see also next chapter)