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This is chapter 37 problem number 50.
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We have a particle that is under the effective force that is directed from the positive x -axis 30 degrees.
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But what we're asked is actually the direction of acceleration that the particle is experiencing when it is moving, when the particle is moving in the positive x direction.
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At a speed that is around 70 % of the speed of light.
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So at that instant, we want to know the direction of the acceleration.
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So the force has obviously two components, right? the component of the force, let's get rid of this velocity here.
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But let's talk about the x component of the force, f sub -x we're going to call it, and the y component of the force, we're going to call it f -sy -y.
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Now, in our case, f sub -x is going to be responsible for generating the acceleration in the x direction.
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So when, you know, if we didn't have a relativistic approach, we would do m times a, but we can't do that anymore because our speed is very high.
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So then i suggest that you go and visit the equation 37 .32 on your textbook that you're going to see if the force is along the velocity vector, then the relativistic force is going to be gamma cubed times m, m being the rest mass, of course.
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This is only for the motion, only for the force if your force is along the direction of the velocity vector.
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This is what is happening in the x direction.
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However, in the y direction, as you can see, this is independent.
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Of the direction of the velocity vector.
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So again, equation 3732 tells you, then the force is going to be gamma factor times, the rest mass, times the acceleration in that particular direction.
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So we have two different components to figure out.
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Now, if we're going to know what a sub -x is, right, we can divide both sides by gamma -cube times a, gamma cube times m.
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Gamma cube times m.
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So then we're isolating a subx, f subx divided by gamma cubed times m.
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We said, well, from trigonometry here, f subx is going to be equal to cosine 30 times the f vector.
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So f cosine 30 over gamma cubed.
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So let's leave the gamma cube.
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Aside let's write down the mass here the rest mass gamma cubed let me give you a reminder here gamma is one over square root of one minus v squared over c squared since we have the gamma in denominator i'm going to actually flip this and i'm going to add it as a multiple into the equation so it's going to be square root of one minus v squared over um c squared cubed so from here since we're not given f or m, i'm going to leave my answer in terms of f over m, but i can calculate the gamma portion...