The center-of-mass framework helps to easily describe the work done on rigid bodies. Since the internal forces in a rigid body do no work, they can be ignored, and the external forces can be considered in the work-energy theorem.
The work done by gravity to move a rigid body, or the work done by an opposing force to move a rigid body against gravity, can be calculated using the center-of-mass framework. It is the line integral of the force of gravity over the path, considered positive if...

When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...

Gravitation is one of the four fundamental forces in nature. The force between objects on Earth and Earth itself is called gravity.
Like other forces, gravity does work on an object if it displaces it toward the Earth's center. In this case, the work done by gravity is said to be positive. If an external force acts on the object against the pull of gravity and manages to lift it away from the Earth's center, work is done against gravity. In this case, the net work done is said to be...

Dry friction occurs between two solid surfaces in contact as they attempt to move relative to one another. In daily life, dry friction is encountered in various forms, such as when walking on the ground, sliding an object across a table, or rubbing hands together. Despite its ubiquity, the underlying mechanisms behind dry friction are not readily visible.
To illustrate this concept, imagine a wooden crate resting on a rough, non-uniform horizontal surface. When an external force is applied to...

In mechanics, work is done on an object when the force acting on it displaces the object. In thermodynamics, work done on a system can be estimated when the system's volume changes during any thermodynamic process.
Consider a gas confined to a cylinder fitted with a movable piston at one end. If the gas expands from volume V1 to volume V2, it exerts a force on the piston, such that the piston moves by a distance dr.
The work done by the gas on the piston can be expressed as

When freshly poured concrete is exposed to freezing temperatures before it has set, the water within the concrete can freeze. This expansion disrupts the setting process, delays chemical reactions necessary for hardening, and increases the volume of pores within the hardened concrete, which weakens its overall structure. If the concrete manages to reach an appreciable strength before it freezes, the damage can be somewhat mitigated.
To counteract the negative impacts of cold weather, ensuring...