Answer :
Answer:
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
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; [tex]m_w = 8.00kg[/tex]
Density of wood; [tex]\delta _w = 696 kg/m^3[/tex]
Density of lead; [tex]\delta _{Ld} = 11340 kg/m^3[/tex]
Density of water; [tex]\delta _{water} = 1000kg/m^3[/tex]
First we determine the volume of wood:
[tex]v_w = \frac{mass}{density} = \frac{m_w}{\delta w} = \frac{8.00kg}{696kg/m^3}\\\\v_w = 0.01149m^3[/tex]
Now, using Archimedes principle:
Buoyancy force is determined using the equation:
[tex]F_b = V * \delta * g[/tex]
Where:
- [tex]F_b[/tex] is the buoyancy force acting on the object
- V is the submerged volume of the object
- [tex]\delta[/tex] is the density of the fluid the object is submerged in( Density of water; [tex]\delta _{water} = 1000kg/m^3[/tex])
- g is the force of gravity( [tex]9.8m/s^2[/tex])
We substitute our values into the equation
[tex]F_b = 0.01149m^3\ *\ 1000kg/m^3 * 9.8m/s^2\\\\F_b = 112.602 kg.m/s^2\\\\F_b = 112.602N[/tex]
Now, buoyancy force [tex]F_b[/tex] = Weight + Tension
[tex]F_b = mg + T\\\\T = F_b - mg[/tex]
We substitute in our values
[tex]T = 112.602N - ( 8kg * 9.8m/s^2)\\\\T = 112.602N - 78.4kgm/s^2\\\\T = 112.602N - 78.4N\\\\T = 34.2N[/tex]
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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