Referring to Figure 11.21, prove that the buoyant force on the cylinder is equal to the weight of the fluid displaced (Archimedes' principle). You may assume that the buoyant force is F 2 − F 1 and that the ends of the cylinder have equal areas A . Note that the volume of the cylinder (and that of the fluid it displaces) equals ( h 2 − h 1 ) A . Figure 11.21 (a) An object submerged in a fluid experiences a buoyant force F B . If F B is greater than the weight of the object, the object will rise. It F B is less than the weight of the object, the object will sink. (b) If the object is removed, it is replaced by fluid having weight W f 1 . Since this weight is supported by surrounding fluid, the buoyant force must equal the weight of the fluid displaced. That is, F B =w f l , a statement of Archimedes' principle.
Referring to Figure 11.21, prove that the buoyant force on the cylinder is equal to the weight of the fluid displaced (Archimedes' principle). You may assume that the buoyant force is F 2 − F 1 and that the ends of the cylinder have equal areas A . Note that the volume of the cylinder (and that of the fluid it displaces) equals ( h 2 − h 1 ) A . Figure 11.21 (a) An object submerged in a fluid experiences a buoyant force F B . If F B is greater than the weight of the object, the object will rise. It F B is less than the weight of the object, the object will sink. (b) If the object is removed, it is replaced by fluid having weight W f 1 . Since this weight is supported by surrounding fluid, the buoyant force must equal the weight of the fluid displaced. That is, F B =w f l , a statement of Archimedes' principle.
Referring to Figure 11.21, prove that the buoyant force on the cylinder is equal to the weight of the fluid displaced (Archimedes' principle). You may assume that the buoyant force is
F
2
−
F
1
and that the ends of the cylinder have equal areas A. Note that the volume of the cylinder (and that of the fluid it displaces) equals
(
h
2
−
h
1
)
A
.
Figure 11.21 (a) An object submerged in a fluid experiences a buoyant force FB. If FB is greater than the weight of the object, the object will rise. It FB is less than the weight of the object, the object will sink. (b) If the object is removed, it is replaced by fluid having weight Wf1. Since this weight is supported by surrounding fluid, the buoyant force must equal the weight of the fluid displaced. That is, FB=wfl, a statement of Archimedes' principle.
A block of mass 0.85 kg and density 600 kg/m3 is forced under the surface of the water by means of a spring (k =
90.0 N/m) that is fixed to the bottom of the container. How much does the spring stretch? (the
density of water is 1000 kg/m3).
Given: A person is diving in a lake in the depth of h = 8.5 m. The density of the water is ρ = 1.0 x103 kg/m3. The pressure of the atmosphere is P0 = 1.0 x 105 Pa. The surface area of the top of the person's head is A = 0.0485 m2
Express the absolute pressure at the depth of h, P, in terms of P0, ρ, and h.
Calculate the numerical value of P in Pa
Express the magnitude of the force exerted by water on the top of the person's head F at the depth h in terms of P and A.
Calculate the numerical value of F in N.
The differential change in pressure p close to the surface of a static fluid is given by the following expression: dp/dy = -3Ap2,where A is a constant, with units of 1/(atm•m), and p is the pressure in atm. The pressure at the surface of the fluid is p(0) = 1 atm, and the coordinate y here is positive upwards with origin at the surface.
Write an expression for the absolute pressure as a function of y.
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