A large rock (specific gravity = 2.25) is submerged in water and suspended from

Question

A large rock (specific gravity = 2.25) is submerged in water and suspended from a wire attached to the end of a rigid beam, as shown below. The system is in equilibrium when the beam is horizontal. Determine the weight of the rock.

A large rock (specific gravity = 2.25) is submerged in water and suspended from a wire attached to the end of a rigid beam, as shown below. The system is in equilibrium when the beam is horizontal. Determine the weight of the rock.

The answer should be: 216 lbf, but need some explanation. Thanks.

Explanation / Answer

Let:

Fb: be the boyance force

F: be the tension in the wire

W: be the weight of the rock:

rho_r: density of rock

rho_w: density of water

V: volume (Note that the volume is the same for the rock and the water: the displace volume of water)

At equilibrium : W = Fb + F

First find F, the tension in the wire by doing moment balance around the pin.

(300)(4) = (10)*F so F= 120;

rho_r = 2.25 * 62.4 = 140.4

Now,

(rho_w)(g)(V) + F = (rho_r)(g)V

62.4 gV + 120 = 140.4 gV

=> gV = 1.5385

Use gV to find Fb.

Fb= (rho_w)(gV) = (62.4)(1.5385)=96 lbf

Weight of rock = Fb + 120 = 216 lbf

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