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Power is the rate with respect to time at which work is done; it is the time derivative of work: =, where P is power, W is work, and t is time.. We will now show that the mechanical power generated by a force F on a body moving at the velocity v can be expressed as the product: = =
This velocity is the asymptotic limiting value of the acceleration process, because the effective forces on the body balance each other more and more closely as the terminal velocity is approached. In this example, a speed of 50 % of terminal velocity is reached after only about 3 seconds, while it takes 8 seconds to reach 90 %, 15 seconds to ...
Newton's laws are often stated in terms of point or particle masses, that is, bodies whose volume is negligible. This is a reasonable approximation for real bodies when the motion of internal parts can be neglected, and when the separation between bodies is much larger than the size of each.
The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them: [11] Diagram of two masses attracting one another = where F is the force between the masses; G is the Newtonian constant of gravitation (6.674 × 10 −11 m 3 ⋅kg −1 ⋅s −2);
Settling velocity W s of a sand grain (diameter d, density 2650 kg/m 3) in water at 20 °C, computed with the formula of Soulsby (1997). When the buoyancy effects are taken into account, an object falling through a fluid under its own weight can reach a terminal velocity (settling velocity) if the net force acting on the object becomes zero.
When considering atmospheric or oceanic dynamics, the vertical velocity is small, and the vertical component of the Coriolis acceleration () is small compared with the acceleration due to gravity (g, approximately 9.81 m/s 2 (32.2 ft/s 2) near Earth's surface). For such cases, only the horizontal (east and north) components matter.
The discovery of the linear relationship between redshift and distance, coupled with a supposed linear relation between recessional velocity and redshift, yields a straightforward mathematical expression for Hubble's law as follows: = where v is the recessional velocity, typically expressed in km/s.
The ancient Greek understanding of physics was limited to the statics of simple machines (the balance of forces), and did not include dynamics or the concept of work. During the Renaissance the dynamics of the Mechanical Powers, as the simple machines were called, began to be studied from the standpoint of how far they could lift a load, in addition to the force they could apply, leading ...