For this problem, please provide numerical answers to two significant figures us

Question

For this problem, please provide numerical answers to two significant figures using scientific notation in the form "1.2e3" (for 1200).

In 1690, Sir Edmund Halley (of comet fame) invented the diving bell. A drawing is shown below. Halley's bell was approximately a wooden cylinder about 3 m high and 1 m in diameter. (For this problem, treat the bell as if it were a cylinder of the indicated dimensions.)

(a) If the bottom of the bell is held by a rope so that it is completely submerged, with the bottom of the bell hovering just above the mud at the bottom of a freshwater lake 20 m below the surface, what is the force the water is exerting on the top of the bell? _____ N

(b) What is the force the water is exerting on the bottom of the bell? _____ N

(c) If the bell and its contents have a mass of 800 kg, how big a weight has to be added to the bell as ballast in order to keep it from floating up to the surface? ____ N

Explanation / Answer

pressure at a depth of h m in water is given as

P=atmospheric pressure+density of water*g*depth

=101325+1000*9.8*h

when the bell is completely at the bottom of the lake,

then the top is at a depth of 20-3=17 m

pressure=101325+1000*9.8*17

=267925 Pa

then force on the top=pressure * area

=267925*pi*radius^2

=267925*pi*(1/2)^2

=2.1043*10^5 N

in scientific notation, force =2.10e+5 N

part b:

at the bottom, depth=20 m

pressure=101325+1000*9.8*20

=297325 N/m^2

force at the bottom=297325*pi*(1/2)^2

=2.34e+5 N

part c:

let mass of ballast required is m kg.

then total weight =(m+800)*9.8 N

this force has to be greater than the buoyant force so that the bell will be remain submerged.

==>volume of the cylinder*density of water*9.8=(m+800)*9.8

==>pi*(1/2)^2*3*1000=m+800

==>2356.2=m+800

==>m=1556.2 kg

hence the weight required=1556.2*9.8=1.52e+4 N

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