When an object is dropped, it accelerates toward the center of the Earth. If the net external force on the object is its weight, it is said to be in free fall; that is, the only force acting on the object is gravity. Galileo was instrumental in showing that, in the absence of air resistance, all objects fall with the same acceleration g. However, when objects on the Earth fall downward, they are never truly in free fall, because there is always some upward resistance force from the air acting...

True weight is the measure of the gravitational force acting on an object. However, if the object accelerates, its measured weight is different from its true weight. Similar observations can be made when the object is submerged in water. An object's weight in water is its apparent weight, which is equal to the difference between its true weight and the buoyant forces.
Consider a person standing on a bathroom scale inside an elevator. If the scale is accurate at rest, its reading equals the...

Stormwater detention basins are essential in managing runoff during heavy rainfall, particularly in urban areas where impervious surfaces increase the risk of flooding. Understanding the conservation of mass in these systems allows engineers to optimize basin performance, balancing inflow, outflow, and water storage.
In the context of a detention basin, the conservation of mass states that the total mass of water entering the basin must equal the mass leaving the basin plus any accumulation of...

All objects, neglecting air resistance, fall with the same acceleration towards the Earth's center due to the force exerted by the Earth's gravity. This experimentally determined fact is unexpected because we are so accustomed to the effects of air resistance and friction that we expect light objects to fall slower than heavier ones. People believed that a heavier object had a greater acceleration when falling until Galileo Galilei (1564–1642) proved otherwise. We now know this is...

Consider a system comprising several point masses. The coordinates of the center of mass for this system can be expressed as the summation of the product of each mass and its position vector divided by the total mass:

The principle of conservation of mass is fundamental in fluid dynamics and is crucial for analyzing flow within fixed control volumes, such as pipes or ducts. This principle states that the total mass within a control volume remains constant unless altered by the inflow or outflow of mass through the control surfaces. This results in a vital relationship for steady, incompressible flow where the mass entering a system equals the mass leaving it.
In the case of a sewer pipe, which can be modeled...