A machine that is strong enough to apply a big force to cause a displacement in a small mount of time (i.e., a big velocity) is a powerful machine. A powerful lineman on a football team is strong and fast. A powerful weightlifter is strong and fast. A powerful piece of farm equipment is strong and fast. A powerful car engine is strong and fast.

This new equation for power reveals that a powerful machine is both strong (big force) and fast (big velocity). Since the expression for velocity is displacement/time, the expression for power can be rewritten once more as force*velocity. And since the expression for work is force*displacement, the expression for power can be rewritten as (force*displacement)/time. With these two approximations, Ben's power rating could be determined as shown below.Д«en's power rating is 871 Watts. It can also be assumed that the angle between the force of the stairs on Ben and Ben's displacement is 0 degrees. By so doing, the stairs would push upward on Ben's body with just enough force to lift his body up the stairs. It can be assumed that Ben must apply an 800-Newton downward force upon the stairs to elevate his body. If this were the case, then we could calculate Ben's power rating. Suppose that Ben Pumpiniron elevates his 80-kg body up the 2.0-meter stairwell in 1.8 seconds. Thus, the weight of the student is equal to the force that does the work on the student and the height of the staircase is the upward displacement.

Despite the diagonal motion along the staircase, it is often assumed that the horizontal motion is constant and all the force from the steps is used to elevate the student upward at a constant speed. A common physics lab involves quickly climbing a flight of stairs and using mass, height and time information to determine a student's personal power. That is, some people are capable of doing the same amount of work in less time or more work in the same amount of time. Some people are more power-full than others. The power equation suggests that a more powerful engine can do the same amount of work in less time.ДЄ person is also a machine that has a power rating. The point is that for the same amount of work, power and time are inversely proportional. That is, a 160-horsepower engine could accelerate the same car from 0 mi/hr to 60 mi/hr in 4 seconds. If this were the case, then a car with four times the horsepower could do the same amount of work in one-fourth the time. Suppose that a 40-horsepower engine could accelerate the car from 0 mi/hr to 60 mi/hr in 16 seconds. The power rating relates to how rapidly the car can accelerate the car. A car engine is an example of a machine that is given a power rating. Thus, the power of a machine is the work/time ratio for that particular machine. The power rating indicates the rate at which that machine can do work upon other objects. All machines are typically described by a power rating. Most machines are designed and built to do work on objects. One horsepower is equivalent to approximately 750 Watts. For historical reasons, the horsepower is occasionally used to describe the power delivered by a machine. Thus, a Watt is equivalent to a Joule/second. As is implied by the equation for power, a unit of power is equivalent to a unit of work divided by a unit of time. The standard metric unit of power is the Watt. Mathematically, it is computed using the following equation. The hiker has a greater power rating than the rock climber. The quantity that has to do with the rate at which a certain amount of work is done is known as the power. The two people might do the same amount of work, yet the hiker does the work in considerably less time than the rock climber. On the other hand, a trail hiker (who selects the easier path up the mountain) might elevate her body a few meters in a short amount of time. For example, a rock climber takes an abnormally long time to elevate her body up a few meters along the side of a cliff. Sometimes, the work is done very quickly and other times the work is done rather slowly. Work has nothing to do with the amount of time that this force acts to cause the displacement. The quantity work has to do with a force causing a displacement.

Power to the people machine