A lead block is suspended by means of a string from the underside of a 8.00 kg block of wood of density of 696 kg/m3. If the upper surface of the wood is just level with the water, what is the tension in the string?(The density of lead is 11340 kg/m3)

If the upper surface of the wood is just level with the water, the tension in the string is 34.2 Newton.

Mass of block of wood;

Density of wood;

Density of lead;

Density of water;

First we determine the volume of wood:

Now, using Archimedes principle:

Buoyancy force is determined using the equation:

Where:

We substitute our values into the equation

Now, buoyancy force = Weight + Tension

We substitute in our values

Therefore, if the upper surface of the wood is just level with the water, the tension in the string is 34.2 Newton.

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Tension of rope T = 35.16 N

Explanation:

Given:

Mass of block = 8 kg

Wood of density = 696 kg/m³

Density of lead = 11,340 kg/m³

Find:

Tension in the string

Computation:

Volume of wood = Mass of block / Wood of density

Volume of wood = 8 / 696

Using Archimedes law

Mw + M  = (Vw + V) 1,000

8/1,000 + 11,340v = (Vw + V) 1,000

V = 3.47 x 10⁻⁴

Tension of rope T

T = v (11,340 - 1,000)9.8 N

T = (3.47 x 10⁻⁴)(11,340 - 1,000)9.8 N

Tension of rope T = 35.16 N