Chapter 11, Problem 52PE

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 $\left(h_2-h_1\right)A$ .

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_f1. Since this weight is supported by surrounding fluid, the buoyant force must equal the weight of the fluid displaced. That is, F_B=w_fl, a statement of Archimedes' principle.