If the shape of an object is altered, the center of gravity may move closer to the heavier side, depending on the distribution of mass.

In the bending process, material is bent around a specific radius.

Shrinkage refers to the reduction in volume of the metal as it cools and solidifies, which can lead to defects.

The acceleration due to gravity near the Earth's surface is approximately 9.81 m/s².

An object moving in a circular path at constant speed experiences centripetal acceleration directed towards the center of the circle.

The angle θ can be found using tan(θ) = μs. Thus, θ = arctan(0.4) ≈ 21.8 degrees.

For a uniform beam, the center of gravity is located at its midpoint, which is L/2.

For a uniform beam, the center of gravity is located at the midpoint of the beam.

For a uniform rectangular plate, the center of gravity is located at the geometric center.

The coefficient of static friction (μs) can be calculated using the formula F = μs * N, where N is the normal force. Here, N = mg = 50 kg * 9.81 m/s² = 490.5 N. Thus, μs = F/N = 200 N / 490.5 N ≈ 0.4.

For a rigid body to be in static equilibrium, both the sum of all forces and the sum of all moments acting on the body must be zero.

An object is in static equilibrium when both the sum of forces and the sum of moments acting on it are zero.

The critical load P = (π² * E * I) / (L²). Substituting the values: P = (π² * 200e9 * 0.0001) / (3²) = 1.96 kN.

The critical load for buckling of a column fixed at both ends is given by P_cr = π²EI / L².

Entropy is defined as a measure of disorder or randomness in a system, reflecting the number of microscopic configurations that correspond to a thermodynamic system's macroscopic state.

Yield strength is defined as the stress at which a material begins to deform plastically, meaning it will not return to its original shape.

As the angle of inclination increases, the normal force acting on the object decreases.

Increasing the moment of inertia decreases the bending stress in a beam for a given bending moment.

The efficiency of a Carnot engine is given by the formula 1 - (T_c / T_h), where T_h is the temperature of the hot reservoir and T_c is the temperature of the cold reservoir.

Stress is defined as the force applied per unit area, hence the formula is Stress = Force / Area.

The bending stress in a beam is calculated using the formula σ = My/I, where M is the bending moment, y is the distance from the neutral axis, and I is the moment of inertia.

The deflection (δ) of a cantilever beam with a point load (P) at the free end is given by δ = PL³ / 3EI.

The frictional force is calculated using the formula F_friction = μN, where μ is the coefficient of friction and N is the normal force.

The moment of inertia for a rectangular beam is given by the formula I = (b * h^3) / 12, where b is the base width and h is the height.

Stress is defined as the force applied per unit area, hence the formula is Stress = Force / Area.

CNC machining offers increased precision and repeatability due to its computer-controlled operations.

The main advantage of using a Carnot engine is that it operates at maximum efficiency, as it is an idealized engine.

CNC machines offer greater precision and repeatability compared to manual machining processes.

Die casting provides high dimensional accuracy, making it suitable for complex shapes.

Laser welding offers high speed and precision, making it suitable for intricate welds.