A 500 g hollow sphere is attached to a uniform metallic stick of mass 1 kg and length 1 m. The sphere can slide freely along the stick. Initially, the stick lies along the x-axis. Suppose you set the sphere at distance x from the right-hand end of the stick. Find x if the position of the center of mass of the composite system is 36 cm from the right-hand end of the stick.

Consider a scenario, in which three distinct spherical masses are joined together by a rigid bar of negligible mass. Determine the coordinates of the center of mass for this configuration.

A delivery vehicle, measuring 4.1 m in height and 2.6 m in width, has its center of gravity located 2.5 m above the ground due to its cargo arrangement. What is the maximum inclined angle at which the vehicle can be parked without risking tip-over?

A new skyscraper is being constructed in the city center. The tower is planned to rise to a height of 300 m with a base measuring 60 m × 80 m. The total mass of the building is estimated to be around 2.5×10⁷ kg, resulting in a weight of approximately 2.5×10⁸ N. Given a forecasted wind speed of 250 km/h, which is expected to exert a force of 1100 N/m² over the 80-meter-wide face, calculate the torque around the potential pivot point located at the rear edge of the building. Assume the total force of the wind acts at the midpoint of the building's face and that the building lacks anchoring into bedrock. The force F_g is the force exerted by the ground when the skyscraper just begins to tip.

An 8.0×10⁴ kg aircraft is orbiting Earth at a constant velocity. The forces acting on it are depicted in the figure below. The thrust generated by the onboard propulsion system is F_w = 7.2×10⁵N, acting on a line 1.8 m below the aircraft's center of mass. Calculate the drag force $F_D$ exerted by the atmosphere and the distance above the center of mass where it acts. Assume that both F_D and F_W are horizontal. (F_lift represents the lift force generated by the aircraft's wings, if any.)

An object of irregular shape is placed on a horizontal massless surface supported by two identical scales, one placed under its left edge and the other under its right edge. The readings on the scales are 60.2 kg and 55.8 kg, respectively. Calculate the distance from the left edge of the object to its center of gravity if the horizontal length of the object is 1.65 m.