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Buoyancy and Stability Problem

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Questions and Answers

What is the direction of the external force required to keep the bronze cube in equilibrium?

Horizontal
Downward
Unknown direction
Upward (correct)

What is the number of forces acting on the cube in the vertical direction?

4
5
3 (correct)
2

Where does the weight of the cube act?

Through its centroid
Through its center of gravity (correct)
Through its top surface
Through its bottom surface

What is the purpose of drawing a free-body diagram?

To visualize the forces acting on the cube (D) Signup and view all the answers

What would happen to the bronze cube if no external force is applied?

It would tend to sink in water (B) Signup and view all the answers

What is the direction of the buoyant force acting on the cube?

Upward (A) Signup and view all the answers

What is the purpose of assuming an upward force in the free-body diagram of the cube?

To hold the cube in equilibrium (C) Signup and view all the answers

How is the weight of the cube calculated?

w = γBV (D) Signup and view all the answers

What is the displaced volume of the cube in the water?

0.123 m3 (A) Signup and view all the answers

What is the purpose of solving the equation algebraically for the desired term in Step 4?

To find the external force (C) Signup and view all the answers

What is the specific weight of the water in the problem?

9.81 kN/m3 (D) Signup and view all the answers

What is the significance of the positive result in Part a of the solution?

The buoyant force is greater than the weight of the cube (A) Signup and view all the answers

What is the magnitude of the force required to hold the block of bronze in equilibrium under water?

9.63 kN (B) Signup and view all the answers

What is the purpose of drawing a free-body diagram in this problem?

To determine the magnitude and direction of the external force required to hold the cube in equilibrium (B) Signup and view all the answers

What is the difference between the two free-body diagrams shown in Fig. 5.3?

The direction of the external force is different (B) Signup and view all the answers

How can the magnitudes of w and Fb be calculated?

By using the equation of equilibrium (A) Signup and view all the answers

What is the purpose of using two free-body diagrams in this problem?

To demonstrate that the solution is independent of the assumed direction of the external force (A) Signup and view all the answers

What is the weight of the cube in this problem?

Calculated in part (a) of the problem (C) Signup and view all the answers

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