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 steel wire of $5.65\text{ mm}$ diameter and $50\text{ m}$ length is used for a hoisting crane. The wire is used to vertically lift a weight of $200\text{ kg}$ attached to its lowest end. Assume the Young's Modulus of Elasticity of Steel as $2 \times 10^5\text{ N/mm}^2$ and gravitational acceleration as $10\text{ m/sec}^2$. The elongation of the steel wire (in mm ) will be ______ [rounded off to two decimal places].
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 load of 30 kN is applied vertically downward at the free end of a cantilever of span 5 m. If the elastic modulus of the cantilever is 30 GPa and the section has a width of 0.3 m and a depth of 0.6 m, then, the elastic deflection (in mm) is ________
- A solid straight steel rod of diameter 100 mm is bent in single curvature into a circular arc by a moment of 50 kNm applied at its ends. If elastic modulus, E, for steel is $2 \times 10^5$ MPa, the radius of curvature (mm) of the arc assuming $\pi=3.14$ is ________
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______
