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(I) A 7150-kg railroad car travels alone on a level frictionless track with a constant speed of 15.0 m/s. A 3350-kg load, initially at rest, is dropped onto the car. What will be the car's new speed?
I) How much tension must a rope withstand if it is used to accelerate a 1210-kg car horizontally along a frictionless surface at 1.20 m/s$^2$ ?
(II) A person has a reasonable chance of surviving an automobile crash if the deceleration is no more than 30 $g$'s. Calculate the force on a 65-kg person accelerating at this rate.What distance is traveled if brought to rest at this rate from 95 km/h?
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welcome to the next section in traveling waves in this section, we're going to consider to new materials that we're gonna have waves propagating through. Um and they're both things you've seen before. So you maybe haven't thought of in this context. The first we're going to think about is sound waves, sound waves. So what is the medium that sound travels through? Well, usually it's air. Um, sound can also travel through liquid to in fact, though, eh? So we're just gonna say that sound travels through fluids, Okay, so sound waves travel through fluid, and what they do is that they're actually an alternating high pressure low pressure system. So you have a band of high pressure, then you have a band of low pressure, and it's not a discreet step here like I'm drawing. It's actually and so on so forth. If I were to draw pressure as a function of position here or a time even because remember, it's a function of both, it would oscillate like this. So you have high pressure and low pressure around not zero, but some central standard pressure peanut that it was already at before the wave traveled through it. Okay, so this is a pressure wave that travels through the system. It's known as a longitudinal wave, because what we're doing is to increase the pressure. We squeeze particles together to reduce the pressure, we pull particles away from each other. So high pressure, low pressure, high pressure, low pressure, high pressure. We still have lambda and we still have a frequency. So all the properties of waves air here. It's just a different material. So how do we deal with this? Um, well, as before, the speed of sound speed through which it travels through this is dependent on the material it travels through. And it looks something like this. What this is is B is the bulk module ISS, which is a measure of how much you can compress the material, how much you can compress the fluid and how hard it will push back. And then row is the mass density. So that's gonna be masked in a particular volume. So, for example, if you had a cubic meter and could way that to find the mass, then you could take that mass divided by the volume to find the density this is used were using the Greek letter wrote to designate this. Okay, so, um, this is very helpful because it lets you deal with a lot of different types of fluids in different conditions, and you can either solve for the bulk module lists or plug in the bulk module is empirically and predict the speed of sound through it. However, it's not very useful for standard problems. So what we're gonna use is an empirical equation, meaning it came from data which looks like this. It says Speed of sound is equal to 331 m per second times the square root of the temperature in degrees Celsius plus 2, 73. And of course, this would have to be degrees Celsius divided by 2 73 degrees Celsius. Okay, Um, now, this isn't quite correct. Here is in terms of the units, because again, it's an empirical equation. What we need is the speed of sound. You can see clearly the units will cancel, so it's not too important. But what we're trying to say is here that to 73 which some of you may recognize as zero degrees Celsius. Um, just as we go above or below that we're going to change our speed of sound now. This only works at the surface of the earth, okay? With our particular atmosphere. So don't try to use it anywhere else. It would be wrong, but it is corrected the surface of the earth. And it's particularly with the scaling factor. And we can watch how speed of sound changes with temperature. Okay, um, so moving on, then we've looked at sound waves, which, as I said, is a longitudinal wave. We're also going to look at light waves. If you are aware, light is a wave, it's an electromagnetic wave, okay? And it travels through space. Okay? Literally. It's just traveling through space. Um, and what it looks like is somewhat more complicated because it has this interacting electric and magnetic field. Okay, so we have a new electric field and then perpendicular to it. So coming out of this plane, I'll attempt to draw is a magnetic field. Okay, Which we didn't know it with B. So we have this perpendicular electric and magnetic field that oscillate at back and forth as they travel forward in space. Okay. You don't need to remember that. It's something we'll discuss later on in physics 102 For now, what you need to know is that light waves all travel forward with the same speed which we call C and can be written as one over the square root of these two universal constants, which come from electromagnetism. And again, we'll discuss in physics one or two. But when you type these in, these are the permitted ity and permeability of free space. When you type them in, you get approximately three times 10 to the 8 m per second for this unit. That's all you need to remember is that the speed of light see is equal to three times 10 to the 8 m per second. Now you may be getting annoyed because I keep introducing variables. But I'll tell you right now you've seen see before. If you've ever heard of Einstein's equation E equals M c squared, it's that c Okay, speed of light squared is what shows up in Einstein's equation, and it's what we have here. So we have this speed of light for our light waves, and we have this speed of sound for our sound waves. Incidentally, speed of sound when you put it in at room temperature is approximately 343 m per second, which is the default number that I will use in many problems. Okay. S Oh, this is at T equals 20 degrees Celsius. Yeah. Okay, So the last thing we need to talk about here is something that is kind of unusual about light, where light when it passes from free space, That is just space into some materials, say glass or something like that. It will maintain the same frequency, but it will change its wavelength. Okay, It changes its wavelength. So you have some initial wavelength and send some final wavelength. And the reason for that is because we know C is equal to f times. Lambda and F is constant. It's based on the properties of whatever created the light, the star that created the light. Okay. And then Lambda here. So this is a constant and this is a constant. We come into a new material. Lambda changes. Well, what that means is that FNC can't both be constants in the new material. It turns out that what happens is the speed of sound. The speed of light actually changes in the material, so it'll look more like this. Okay, Where speed of light has changed inside the material. Now, we actually use this to classify a property of materials which is called the index of Refraction, where it is the ratio of the speed of light normally to the speed of light inside the material. Now, normally, the speed of light inside the material is going to be significantly less than the speed of light and free space, which means the end will be greater than one. And so most objects you come, interact you interact with, are going to have an index of refraction greater than one. There are a few engineered materials that are made to have indexes of reaction that are less than one. Um and these are kind of unusual materials. We're not going to consider the physics of those materials. In this particular unit, an index of refraction will come up again. Maurin Physics 102 But it does appear in this unit in some physics textbooks
Thermal Properties of Matter
The First Law of Thermodynamics
Kinetic Theory Of Gases
The Second Law of Thermodynamics