A block of metal has a mass of 0.5Kg and density of 8000kg/m3. if it is suspended from a string and completely immerged in water(gw=1000kg/m3). the tension in the string(the answer is 4.375N what are the steps)

Explanation:

Draw a free body diagram.  There are three forces on the block:

Weight force mg pulling down,

Buoyancy force B pushing up,

Tension force T pushing up.

Sum of the forces in the y direction:

∑F = ma

B + T − mg = 0

T = mg − B

Buoyancy is the weight of the displaced fluid:

T = mg − ρVg

The block is fully submerged, so the volume of displaced fluid equals the volume of the block.  The volume of the block is its mass divided by its density.

T = mg − ρ (m/ρₓ) g

T = mg (1 − ρ/ρₓ)

Plug in values and solve.

T = (0.5 kg) (10 m/s²) (1 − (1000 kg/m³) / (8000 kg/m³))

T = (5 N) (1 − ⅛)

T = 4.375 N

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