This topic is a relationship between power and work.

## What is Work?Edit

In physics, work has a very specific meaning.

Work is the transfer of energy as a result of applying a force over a distance. Therefore to calculate work, you multiply the force by the distance the object moves in the direction of the force. If you lift a block with a weight of one newton for a distance of one meter, you do one joule of work. Work is done on objects. If you lift a block one meter with a force of one newton, then you have done one joule of work *on the block. *It is important to remember in the calculation of work that the force and distance are in the same direction. Not all force does work. If you push down a book on the table, you have done zero work because despite the force you applied, the distance is zero as the book didn't move downward through the table.

## What is Power?Edit

Same amount of work can be done as long as same amount of force is applied and same amount of distance is traveled. However, one can do the same amount of work faster than others. Thus that someone is more powerful than others because power is the rate at which work is done, or energy flows.

Power equals to work divided by time. Because work's unit is joules and time's unit is seconds, one watt of power equals to one joule per second. Another unit of power that is often used for engine power is horsepower. One horsepower is euqal to 746 watts.

## Real World SituationEdit

Power and work are involved in everyone's daily life. Human

power is a real world connection to this topic. The maximum power output of a person is typically around a few hundred watts at the peak. But over time, our biological bodies experience stress in doing the work and eventually power decreases. Highly trained athletes can keep up a power of 350 watts for about an hour while an average person produce an average power of around 200 watts through an hour of running and biking. Human power is directly related to fitness and health. We have calculated our own powerfulness in physics class where we first found our mass using the scale, and then we all run up the same amount of stair cases to do the same amount of work but with different time. Then using the equations of work and power we found our own power and compared it in class with others’ results.

## Word ProblemsEdit

### Roller Coaster

A roller coaster with a total mass of 20,000 kg travels up a 70-meter hill in 40 seconds. How powerful is the roller coaster's motor?

In this problem we are asked for the power. We are given the mass in kilograms, the time in seconds, and the height in meters. We know from our understandings of power and work that power equals to work divide by time while work equals to force times distance. We also know from knowledge that the force of gravity can be found by multiplying the mass of the object with the gravitational acceleration.

So to find power we must first find work. The weight of the roller coaster is the force and the height of the hill is the distance. F_{g} = (20,000 kg)(9.8 m/sec^{2}) = 196000 N. Then we calculate the work: W = (196000 N)(50m) = 13720000 J. Finally we calculate the power: P = (13720000 J)/(40 sec) = 343000 watts.

### Cart Pushing

Tim pushed a cart with 50 N for 10 meters in 20 seconds. John pushed another cart with 30 N for 50 meters in 30 seconds. Who is more powerful?

In this problem we have two subjects doing different amount of work. This means we have to calculate work and thus power for each of them in order to compare their power. So let’s start with Tim. First we find the work he has done knowing that work equals to force times distance: W = (50 N)(10 m) = 500 J. Then we find his power using the power equation P = W/t: (500 J)/(20 sec) = 25 watts. Now we repeat the same process for John. W = (30 N)(50 m) = 1500 J. P = (1500 J)/(30 sec) = 50 watts. John has a power of 50 watts while Tim has 25 watts. John is obviously more powerful.

## Topic Reflection

The knowledge of power and work has improved my perception of the natural world by giving specific values to things, thus enabling me to see motions and changes systematically in numbers, and finally allowing me to even predict the aftermath of a physical change using power and work. I can now effectively calculate the work one person does and the difference between people’s powers. Power and work are basics in the understanding of simple machines like pulley and levers, which are used in creating complex and literally “powerful” machineries.