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If the ball is thrown upwards, the work done by the gravitational force is negative, and is equal to the weight multiplied by the displacement in the upwards direction. Both force and displacement are vectors. The work done is given by the dot product of the two vectors, where the result is a scalar.
Pressure–volume work (or PV or P-V work) occurs when the volume V of a system changes. PV work is often measured in units of litre-atmospheres where 1 L·atm = 101.325 J. However, the litre-atmosphere is not a recognized unit in the SI system of units, which measures P in pascals (Pa), V in m 3, and PV in joules (J), where 1 J = 1 Pa·m 3.
The sum force acting on the object, then, is equal to the difference between the weight of the object ('down' force) and the weight of displaced liquid ('up' force). Equilibrium, or neutral buoyancy, is achieved when these two weights (and thus forces) are equal.
Work is defined as the force multiplied by the displacement an object moves. The work done on the load is equal to its weight multiplied by the vertical displacement it rises, which is the "rise" of the inclined plane = The input work is equal to the force on the object times the diagonal length of the inclined plane.
The kinetic energy of an object is equal to the work, force times displacement , needed to achieve its stated velocity. Having gained this energy during its acceleration, the mass maintains this kinetic energy unless its speed changes. The same amount of work is done by the object when decelerating from its current speed to a state of rest. [2]
Gravitational "weight" is the force created when a mass is acted upon by a gravitational field and the object is not allowed to free-fall, but is supported or retarded by a mechanical force, such as the surface of a planet. Such a force constitutes weight. [2] This force can be added to by any other kind of force.
The increase in weight is equal to the amount of liquid displaced by the object, which is the same as the volume of the suspended object times the density of the liquid. [1] The concept of Archimedes' principle is that an object immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object. [2]
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: P = d W d t = F ⋅ v {\displaystyle P={\frac {dW}{dt}}=\mathbf {F ...