In order to achieve the static equilibrium of the see-saw about the fulcrum P, shown in the figure, the weight of the Box B should be ________ kg, if weight of Box A is 50 kg.
To achieve static equilibrium of the see-saw about the fulcrum P, the moments on either side of the fulcrum must be equal. The moment is given by the product of the force and the distance from the fulcrum. For this scenario, the force is represented by the weight of the boxes.
Let's denote:
- W_A = weight of Box A = 50 kg
- W_B = weight of Box B (to be determined)
- d_A = distance from fulcrum to Box A = 5 m
- d_B = distance from fulcrum to Box B = 8 m
In equilibrium:
W_A \cdot d_A = W_B \cdot d_B
Substitute the given values:
50 \cdot 5 = W_B \cdot 8
250 = 8W_B
Solve for W_B:
W_B = \frac{250}{8} = 31.25 \text{ kg}
Therefore, the weight of Box B should be 31.25 kg to achieve static equilibrium.
This calculation confirms that the correct answer is 31.25 kg.
Important Questions from Strength of Materials
- A simply-supported steel beam made of an I-section has a span of $8 \text{ m}$. The beam is carrying a uniformly distributed load of $15 \text{ kN/m}$. The overall depth of the beam is $450 \text{ mm}$. The moment of inertia of the beam section is $18000$ cm$^4$. The maximum bending stress in the beam will be _________ N/mm$^2$. [in integer]
A simply supported RCC beam of cross section $0.4 \text{ m} \times 0.6 \text{ m}$ covers a span of $8 \text{ m}$. It is subjected to a uniformly distributed load of $30 \text{ kN/m}$. If the unit weight of concrete is $24 \text{ kN/m}^3$, the tensile stress (in $N/mm^2$, rounded off to two decimal places) at the bottom of the beam at mid-span is______
A rectangular beam section of size 300 mm (width) X 500 mm (depth) is loaded with a shear force of 600 kN. The maximum shear stress on the section in N/mm² is ___________
- A steel I-beam section is subjected to a bending moment of 96 kN-m. The moment of inertia of the beam section is $24,000 \text{ cm}^4$. The bending stress at 100 mm above the neutral axis of the beam in MPa will be ________
A simply supported beam AB has a clear span of 7 meter. The bending moment diagram (BMD) of the beam due to a single concentrated load is shown in the figure below.
The magnitude of the concentrated load in kN is __________.
