A copper block with a density of 8960 kg/m3 is suspended from a string in a beaker of water so that the block is completely submerged but not resting on the bottom. The block is a cube with sides of 4 cm (0.04 m).
- a. What is the volume of the block in cubic meters?
- b. What is the mass of the block?
- c. What is the weight of the block?
- d. What is the buoyant force acting on the block?
- e. What tension in the string is needed to hold the block in place?
(a)
Volume of copper block.
Answer to Problem 3SP
Volume of copper block is
Explanation of Solution
Given info: Density of copper is
Write the equation to find the volume of a cube.
Here,
Substitute
Conclusion:
Volume of copper block is
(b)
Mass of block.
Answer to Problem 3SP
Mass of the copper block is
Explanation of Solution
Write the equation to find the mass.
Here,
Substitute
Conclusion:
Mass of the copper block is
(c)
Weight of the block.
Answer to Problem 3SP
Weight of the copper block is
Explanation of Solution
Write the equation to find the weight.
Here,
Substitute
Conclusion:
Weight of the copper block is
(d)
The buoyant force acting on block.
Answer to Problem 3SP
The buoyant force is
Explanation of Solution
Buoyant force acting on the block is equal to the weight of the water displaced.
Write the equation to find the buoyant force.
Here,
Substitute
Conclusion:
The buoyant force is
(e)
The tension in the string to hold the block.
Answer to Problem 3SP
The tension is
Explanation of Solution
The string in the fluid is acted upon by two forces. They are weight of block down wards and buoyant force upwards.
By Newton’s first law of motion the sum of forces acting on a body must be zero.
Here,
Substitute
Conclusion:
The tension is
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