The person going up the stairs has a weight of 600 N, therefore they are exerting 600 N of force when they go up the stairs. The stairs have a vertical distance of 4m. Work = force x distance, so work = 600 N x 4 m = 2400 Joules. This is how much work they are doing to go up the stairs.
Say you wanted to know how much power they generated walking up the stairs. The equation to use is: power = work / time. The person took 2 seconds to get up the stairs. Power = 2400 J / 2 s = 1200 watts of power. Watts, or J/s, are the units for measuring power. It can also be measured in horsepower which is what we use for the engines of cars, etc. 1 horsepower = 746 watts.
Next we learned about energy, which means "work in" or the ability of an object to do work. Kinetic energy is the energy of movement. You need movement to do work (w = f x d) and KE is measured in Joules. The equation for kinetic energy is: KE = 1/2 m v ^2. The change in KE is equal to work. (∆KE = work). One great application of this information is an alternate way of answering the question why do airbags keep us safe?
When you are in a car crash, you go from moving to not moving regardless of what you hit, therefore the change in kinetic energy is the same regardless of what you hit.
KE = 1/2mv^2
∆KE= KE final - KE initial
∆KE = work
Since the ∆KE is the same and this change is equal to the work done, the work is the same regardless of what you hit. Since work is the same no matter what you hit, the longer of a distance it takes to stop you, the less force is done on you.
work = force x distance
airbag: work = force x distance
dashboard: work = Force x distance
The airbag is soft so it sinks in when you hit it, thus increasing the distance it takes to stop you. Therefore there is a very small force on you, compared to the dashboard which is hard. The less force, the less injury. This is why airbags keep you safe.
My group did our podcast on the relationship between work and kinetic energy. In addition to explaining the infamous airbag problem, we also talked about the change in kinetic energy. Watch the video below for more!
But the energizer bunny never stops and neither does our physics class- especially not when we're talking about work and energy! We also learned about potential energy. PE = mass x gravity x height. Potential energy is the energy of position; if an object has an height, it has potential energy. If an object is at rest it has potential energy (not kinetic because the velocity of an object at rest is 0 m/s so the KE is zero). As an object falls, its potential energy decreases and its kinetic energy increases. A good way to put this is to say that all the potential energy is transferred into kinetic energy. When the object goes back up to its original height, it gains back all of its potential energy. ∆KE = ∆PE. You cannot gain more energy than the amount that you start with. You can, however, lose some of this energy if the object does not have a 100% efficient energy transfer or if there is friction or air resistance. Lost energy is let off as heat, sound, or light. This is why our car engines hum when we drive around- they are very inefficient.
The ball starts with 20 J of PE and 0 J of KE and falls 10 cm. Because ∆PE=∆KE, due to the conservation of energy, and the ∆PE is 20 J, the ∆KE is from 0J to 20J at the bottom of the ball's path. As the ball falls, it loses PE which turns into KE. When it rises back up the opposite happens. Assuming that the ball has 100% efficiency of energy transfer, the ball will rise up 10 cm to its original height because it must go this high to regain all of its PE. If the ball did not have such an efficient transfer, it would lose height.
The picture above shows how roller coasters have conservation of energy even when they have lots of different sizes of hills. As long as all of the hills are smaller than the first one, the potential and kinetic energies will continue to transfer with an equal amount of energy and the roller coaster will keep rolling. (Note: all of the values were made up for this picture and are not exact).
Finally, we learned about machines. Machines were created and designed to make our lives easier. A common misconception is that machines decrease the amount of work we have to do. This is wrong. Machines make it easier for us to do work by increasing the distance over which we do the work so that we can get the same results by exerting less force.
In the picture below, the inclined slope ( a simple machine) increases the distance of the work 4x. The original vertical height is 1 meter and the distance of the machine is 4 meters. This would allow you to only have to use 1/4 of the force. If you are trying to push a 600 N box up the ramp, the ramp makes it so you don't have to use 600 N of force to do this because you are doing the same amount of work in as work out, similar to the conservation of energy. The distance in is 4m, as compared to the distance out of 1m which is how heigh the box is actually lifted although you accomplish this in 4m slanted.
The concept of work in = work out is also similar to the conservation of energy because the work out can never be more than the work in but it can be less than the work in depending on how efficient the machine is. The equation to find the efficiency of the work done is: work out / work in x 100. This should give you a percent efficiency.
What I found the most difficult about what we have studied was the conservation of energy. The transfer from potential to kinetic energy was hard for me to grasp; the roller coaster problem was especially difficult to understand. It confused me how the height increased and decreased again and again but the roller coaster still had the same amount of energy the entire way, even though the amounts of potential and kinetic energy changed depending on its height and position. Drawing the picture in more detail was what helped me finally get it. I am a visual learner through and through. Seeing the different kinetic and potential energies written at the different points of the ride helped me to see that the energies would always add up to the original amount of energy, it was just in different proportions.
At first, it was also hard for me to understand how you could not be doing work on a book that you were carrying if you were moving it forward but now I understand that the force you are doing on the book is vertical because gravity is pulling it down and you are pushing it up (that concept is a bit of a flashback, we learned about action-reaction pairs last semester). You are moving forward so the distance is horizontal and there can be no work because the force and distance are perpendicular and not parallel.
My problem solving skills could have been better in this unit. But I am not too upset that I did not labor over the more difficult problems in this unit. Oftentimes I need a break from a concept before I can understand it. This was definitely true for this unit. When I did not understand the roller coaster problem, I set it aside and came back to it later in more detail and that is when it clicked. However, in the next unit I will spend more time trying to work through the details of harder problems and things that I do not understand. I think this will help me grasp the concepts of the unit in more depth and also allow me to be more engaged in class. I did all of my homework and spent a decent amount of time completing it. I also think I put in a lot of effort to the larger assignments such as blog posts and our podcasts. I got really into finding different ways to present the material- that is why my blog post about machines has two different videos in it. They were both just really cool! And I love Bill Nye, he's great. My confidence in physics faltered a bit this unit, however, as I feel that I did not grasp many of the concepts immediately which is not the case usually. This is another reason why I have a goal of spending more time working through problems in the next unit. I will better understand the material and thus be more confident in my work, which is always a good thing. The airbag problem was one thing that I did not understand at first but through repetition and revisiting it, I finally got it and it helped me with my articulation when writing out and explanation. I have found that using the relevant equations in my explanation really helps me stay on topic and to explain the concept.
This is kind of a stretch, but I connected this unit to every day life because the work that you put into things is the work that you get out, or the results that you see. If i work hard in physics, I will see satisfactory results!
My goals for the next unit are:
1) Bring a positive attitude to class every day.
2) Spend more time on my work (especially hard problems).
3) Study in advance- start reviewing material as soon as we finish one section of the unit. This will be good for the test, the podcast, and our quizzes.
4) Go to conference period to ask Mrs. Lawrence and Mr. Rue for more challenging problems that will help me to further my understanding of the topics and better prepare me for the unit test.
