Physics and Power Help
Introduction to Physics and Power
In the context of physics, power is the rate at which energy is expended or converted to another form. Mechanically, it is the rate at which work is done. The standard unit of power is the joule per second (J/s), more commonly known as the watt (W). Power is almost always associated with kinetic energy. Sometimes the rate at which potential energy is stored is referred to as power.
In the examples shown by Fig. 8-4, the object acquires potential energy when it is lifted, and this potential energy is converted to kinetic energy as the object falls (if it is allowed to fall). The final burst of sound, shock waves, and perhaps outflying shrapnel is the last of the kinetic energy imparted to the object by lifting. Where does power fit into this scenario?
Fig. 8-4 . Work is done when a force is applied over a specific distance. In this case, the force is applied upward to an object against Earth’s gravity.
A slight variation on this theme can be used to talk about power. This is shown by Fig. 8-5. Suppose that instead of a free end of rope, you have a winch that you can turn to raise the object at the other end of the rope. The object starts out sitting on the floor, and you crank the winch (or use a motor to crank it) for the purpose of lifting the object. This, possibly in conjunction with a complex pulley system, will be necessary if you have a heavy object to lift. Then the pulley had better be strong! The same holds true for the rope. And let’s not forget about the manner in which the pulley is anchored to the ceiling.
Fig. 8-5 . Illustration of power. A winch and pulley can be used to life a heavy object.
Let’s Do It!
It will take energy to lift this object. You can crank the winch, imparting potential energy to the object. If the pulley system is complex, you might reduce the force with which you have to bear down on the winch, but this will increase the number of times you must turn the winch to lift the object a given distance. The rate at which you expend energy cranking the winch can be expressed in watts and constitutes power. The faster you crank the winch for a given object mass, the higher is the expended power. The more massive the object for a given winch crank speed, the higher is the expended power. However, the power does not depend on how high the object is lifted. In theory, you could expend a little power for a long time and lift the mass 100 m, 1 km, or 100 km.
Assume that the winch and pulley system is frictionless and that the rope does not stretch. Suppose that you crank the winch at a constant rotational rate. The power you expend in terms of strain and sweat multiplied by the time spent applying it will equal the potential energy imparted to the object. If P is the power in watts and t is the time in seconds for which the constant power P is applied, then the potential energy imparted to the object E p can be found according to this formula:
E p = Pt
This can be rearranged to
P = E p / t
We know that the potential energy is equal to the mass times the acceleration of gravity times the displacement q . Thus the power can be calculated directly by the following formula:
P = 9.8067 mq/t
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