Work
Work can be easily defined as the force exerted on an object over a certain distance. Work is calculated by multiplying force by distance and is measure in Joules (J).
In order to do work on an object, the force and distance must be parallel to each other. For that reason, a server carrying a tray through a dining room is not doing work, but that same server climbing a flight of stairs is doing work.
Work cannot be done if no distance is covered. Anything multiplied by zero is zero, so if you were to push against a wall with no result, no work would be done because the distance covered would be 0m.
Additionally, in questions where a person is climbing the stairs, riding an escalator or an elevator, only the vertical height is relevant.
Here are two examples of work practice problems:
- An actress carries her Oscar across the stage after winning the Academy Award for Best Actress in a Leading Role. The statue weighs 4N and the distance from the stairs to the podium is 4m, how much work does she do?
- A woman walks up the stairs to the stage to accept the Academy Award for Best Director. She weighs 550N and the stairs are 2m high. How much work does she do?
- A server lifts a tray and then carries it to a table. Does he do work when he lifts the tray, when he walks to the table, or both times? Explain.
- The actress does not do any work because the force of the statue and the distance she travels are not parallel, therefore no work can be done.
- work = force*distance; work = 550N*2m; work = 1100J The Academy Award winner for Best Director does 1100 Joules of work.
- The server only does work when he lifts the tray. In this situation, the weight of the tray and the distance it is being lifted are parallel. Therefore, work is being done. Contrarily, when the server carries his tray to the table, the weight of the tray is perpendicular to the distance the server is walking. Therefore, work cannot be done.
Power is defined as how quickly work is done.
It is calculated using: power= work/time. It can be measured using two different units. If you literally translate the units used to measure work/time the unit is J/s (Joules per second). However, power is most commonly measured using Watts (W). Joules per second and Watts are equivalent.
It is likely that you have heard them term Watt before, likely when looking at a light bulb. The amount of power light bulbs generate is measured in Watts. Does 60W sound familiar?
Horsepower is another term that should sound familiar. One horsepower = 746 W.
Now that we know how to calculate both work and power, let's revisit one of our previous problems and add a time component to it.
A woman walks up the stairs to the stage to accept the Academy Award for Best Director. She weighs 550N and the stairs are 2m high. It takes her 10 seconds. How much work does she do? How much power does she generate? Is it enough to power a standard 60W light bulb?
Well, from our calculations above, we already know that she did 1100J of work. We also know that power is equal to work over time. Therefore we can set up our calculations to look like this:
Work = 1100J
Power = work/time
Power = 1100J/10s
Power = 110W
Yes, she did generate enough power the light a 60W light bulb.
Kinetic and Potential Energy
Kinetic energy is the energy of motion. In other terms, it is mass and speed's ability to do work.
It is measured using the formula KE = (1/2)mv^2. It is also measured in Joules.
An object must be in motion to have kinetic energy.
Change in kinetic energy is equal to work. Therefore in the problem we did earlier with the Academy Award winner for Best Director, she did 1100J of work and has 1100J of kinetic energy.
We can use our knowledge of work and energy to tell us why airbags keep us safe.
- You go from moving to not moving regardless of how you stop. Therefore the change in kinetic energy is the same with or without the airbag. Change in kinetic energy is equal to work and work can also be written as distance times force. Therefore, if the distance between you and the force that causes you to stop increases, that force must decrease in order for work to remain constant. The smaller the force of impact is, the less injury will be caused.
- work = F*d or work = F*d
- This is why work remains constant.
- Change in kinetic energy = KE final - KE initial
- work = change in kinetic energy
Potential energy (PE) is the energy of position, and determines the maximum possible kinetic energy an object can have. Consider a pendulum that is about to be released from the highest point of its path. Let's say that it has 200J of potential energy and 0J of kinetic energy here. As soon as it is dropped, the pendulum's potential energy will begin to convert to kinetic energy. When it is halfway between its highest possible and lowest possible points, the pendulum's PE will be equal to 100J and its KE will be equal to 100J. At the lowest possible point on its path, the pendulum will have a PE of 0J and a KE of 200J. Then again, at the highest possible point on the other side, it will have 0J KE and 200J PE.
As shown by this example, an object can be moving and still have potential energy. However, this is only true for PE. An object at rest will never have KE.
PE and KE are why a rollercoaster can complete the track after having been released only once. This is also why no hill on a roller coaster is taller than the first one. The physics reasoning behind this is that the PE that the cars have at the top of the first, tallest hill is the maximum amount of potential energy that the cars can have. Therefore, if no hills are any taller than that first hill, there will always be enough energy to get up and over each one.
Machines
The purpose of a simple machine is to decrease the amount of force you have to use while doing work by increasing the distance you cover. Thus, work in = work out. You can never get more work out of a machine than the amount of work you put in.
For example, if you are moving to a new home and are loading a moving truck-- you can use the amount of work you would do without a ramp to find out how much work you would do with a ramp as long as you know the length of the ramp or the amount of force it would take you with the ramp.
Machines' effectiveness can also be measured. The Law of Conservation of Energy states that energy will always be conserved and that the energy you get out a machine will never be more or less than what you put in. However, a machine can never actually be 100% effective because some of the energy produced must be turned into heat, light or sound. However, the effectiveness of a machine can easily be calculated by setting up a proportion with the amount of Joules of work produced (which will always be the smaller number) over the amount of work you put in.
Here are two helpful videos that talk about machines and include some practice problems.
Niara! This post was amazing, you are very in-depth in your explanations and great at reaching out to an audience beyond Ms. Lawrence, yourself, and our class. I love your visuals and everything is easy to read and understand. Awesome job. You go Glen Coco.
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