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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?
(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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In this video, we begin our investigation of the exact nature of the electric force. French physicist Charles Augustin Nakoula took a charged metal object and attached it with a wire toe on identical metal object that was uncharged. This allows charge the flow from one to the other and because the objects are identical by symmetry, they end up with the exact same charge. You can then disconnect them and they end up with two orbs of unequal charge in each. And we'll call this charge que He then measure the force. Between these charges at some distance are what he found was a certain size force which will just call f not. He then took thes equally charged orbs and he moved him further apart. And if you move these further apart to a distance of say to our, then you'll see that the force between them has changed. And more specifically, it is now f not over four. Mhm. Next he moved. He moved the orbs in relation to each other again. Except this time he placed him closer to each other. So he measures the force between them again. This time the distance is our over to, and what he found was, the force was equal to four F not, and by repeating this again and again and measuring the force between these two equally charged orbs at different distances, he finds that the force is proportional toe one over R. Squared the inverse square of their distance from each other, and you'll notice that this in inverse square law is the same thing that's in. That's obeyed by the gravitational force. Having determined how the distance between two charged objects affects the force, Coolum next investigated how the size of each charge would affect that force. So, using a similar method of charging two equally charge balls, he could take one of those orbs and charge it with another equal one to get half the charge that he originally had. And when he measures this force, he sees that it equals the original force over to, and he could repeat this again and get a ball with a quarter of the charge and find that the force is equal to F not over four. And by repeating this and repeating this, you'll see that the forces linear with the charge and it's linear with each charge. So now our force is proportional to the charge on each orb. And of course, as we've already seen to the inverse square of the distance between them and this leads us to cool arms law. That force is equal to some constant times. The charge on the first object, the charge on the second object, all divided by the distance between them squared. Our next part will investigate more about the nature of this constant of proportionality, k so cool and discovered that the electric force between two charge objects, as we see on the right here, is equal to the charge on the first object times. The charge on the second object divided by the square of the distance between them. Time some constant K in this case is the electric constant, and it has the value of about 8.988 times 10 to the ninth. Newton's times meter squared per Coolum squared que is often also written as one over four pi epsilon. Not where Epsilon not has a value of 8.854 times 10 to the negative 12 Cool, um, squared per newton meters squared the use of either K or Epsilon not is acceptable. Absalon, not is often Ah, lot easier to deal with, depending on what units you're using. But in S I either K or Epsilon not works very well. However, we know that forces a vector and so electrostatic force must also be a vector. So more appropriately, we write that the force of actor is equal decay Q one que two over r squared in the direction of our hat where our hat is just the unit vector in the direction between q one and Q two or more precisely, our hat is simply are divided by the magnitude of our. We'll also notice that if Q One and Q two have the same sign, then if it's positive, if they different different Insein, then our force vector is negative. And so we say that a positive force is repulsive and a negative force is attractive, which we would expect opposite. We charged particles should attract each other and similar, like part charges should repel each other. So we might ask ourselves how strong is the electric force in particular? How strong is it to something we've studied a lot, such as gravity well to answer that. We look at each force. We've shown that the electric force is equal decay. Times Q. One Q two over r squared while the gravitational force will recall is equal to G M one m two over R squared mhm. When we look at the ratio of these, we see that the distance square, the inverse square law drops out because it applies to both the electric force and the gravitational force. And so we're left with Korg Times Q. One Q two over M one M two. Now this leading term a k a. Burgess simply constant. So what will determine the relative sizes of these forces are charges and our masses, and we'll see that for very, very small mass particles such as electrons, protons, atoms, nuclei. This is a very, very small mass, which means that this ratio of the electric force of the gravitational force is very large. And so we expect at small mass objects the electric force will dominate. However, as masters get bigger and bigger, we'll see that the gravitational force begins to dominate and this whole ratio becomes a lot smaller. So the electric force will dominate. When we have small masses and large net charges. Meanwhile, the gravitational force dominates when we get to a larger bodies people, planets, solar systems. In other words, when the masses are much larger than the charges come to further explore in the nature of the electric force versus the gravitational force, we look at the concrete example of the hydrogen atom. So here on the left, we see a typical hydrogen atom which contains a positively charged proton and its nucleus and a Nilla negatively charged electron. At some distance from the nucleus, I've written here all of the constants we need to discuss the gravitational electric forces, the electric constant, the gravitational constant G, the masses of the electron and the proton. And of course, their charges which are equal but opposite in charge and sign. It's also gonna We're also going to need the typical distance between the proton and the electron, which is about half an angstrom or 5.29 times 10 to the L. A. In the meters. This varies in actuality, but that is an average value that we can use for the purposes of this. So we calculate our electric force as the electric, constant times the charge of the electron, the charge of the proton over R squared. And we get something along the lines of 8.24 times 10 to the negative. Eighth eight Newtons. Negative because the forces attractive between them. Our gravitational force, which is G times the masses divided by the distance squared, is 3.63 times 10 to the negative 47 Newton's now. Typically, there is no sign in the gravitational force equation. That's because the force is always attractive. There is no such thing as negative mass so far as we know. And so we'll put a negative sign here to make sure that these agree in concept. We can see if the ratio of these the electric force over the gravitational force is about 2.3 times 10 to the 39. Until that thes scales with these tiny masses on these short distances, the electric force far outweighs the gravitational force. It's only when we get up to macro scales of planets. Uh, solar systems stars that the that the gravitational force will far outweigh the electric force
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