# Power given force and velocity relationship

Power, with units of watts, is the rate at which work is performed or energy is Remember that power is equal to force times velocity (equation (2) above), and. Simply put, force is a change in momentum, with respects to time. . Are you looking for something like power equals force times velocity? That's one way they 're. The quantity work has to do with a force causing a displacement. Thus, the power of a machine is the work/time ratio for that particular machine. is displacement/time, the expression for power can be rewritten once more as force *velocity.

The difference between power and energy is a Calculus idea energy is the time integral of powerbut it's not necessary to understand much Calculus to grasp this idea. For those who want to learn Calculus, click here.

We have decided to lift the previous example's ten-kilogram mass from the table to a high shelf, a distance of three meters. We will compute the required energy first, then discuss power later, for a reason that will become obvious. For a given mass m, a height h over which the mass is to be raised, and a gravitational acceleration g, we compute an energy quantity called workor force times distance, with units of joules: Okay, we have the total energy required, but how much power is needed?

Remember that power is equal to force times velocity equation 2 aboveand energy is power multiplied by time. This means all the solutions below will work: A power of watts for one second. A power of A power of 2. Remember this relationship between power and energy — a small amount of power expended over a long time can accomplish the same task as a large amount of power over a short time.

### Power, Energy & Gravity

But in all cases, the energy required is the same. Potential and Kinetic Energy In simple mechanical systems, energy has two primary forms — potential and kinetic. Potential energy is the energy of position or state — a coiled spring, gas under pressure, a book on a high shelf.

Kinetic energy is energy of motion — an arrow in flight, a weight being lifted, a satellite in orbit. Many mechanical problems turn out to be descriptions of energy conversions — potential to kinetic and back again. The two people might do the same amount of work, yet the hiker does the work in considerably less time 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 hiker has a greater power rating than the rock climber.

Power is the rate at which work is done. Mathematically, it is computed using the following equation. 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.

## Power (physics)

For historical reasons, the horsepower is occasionally used to describe the power delivered by a machine. One horsepower is equivalent to approximately Watts. Most machines are designed and built to do work on objects. All machines are typically described by a power rating. The power rating indicates the rate at which that machine can do work upon other objects.

A car engine is an example of a machine that is given a power rating. The power rating relates to how rapidly the car can accelerate the car.

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. The point is that for the same amount of work, power and time are inversely proportional.

The power equation suggests that a more powerful engine can do the same amount of work in less time. A person is also a machine that has a power rating. Some people are more power-full than others. 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. 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.

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.