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5 March, 23:41

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)

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  1. 6 March, 00:08
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    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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