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Problem 10 Medium Difficulty

An electron is a subatomic particle $\left(m=9.11 \times 10^{-31} \mathrm{kg}\right)$ that is subject to electric forces. An electron moving in the $+x$ direction accelerates from an initial velocity of $+5.40 \times 10^{5} \mathrm{m} / \mathrm{s}$ to a final velocity of $+2.10 \times 10^{6} \mathrm{m} / \mathrm{s}$ while traveling a distance of 0.038 $\mathrm{m}$ . The electron's acceleration is due to two electric forces parallel to the $x$ axis: $\overrightarrow{\mathbf{F}}_{\mathbf{1}}=+7.50 \times 10^{-17} \mathrm{N},$ and $\overrightarrow{\mathbf{F}}_{2}$ which points in the $-x$ direction. Find the magnitudes of $(a)$ the net force acting on the electron and $\quad(b)$ the electric force $\vec{F}_{2}$ .

Answer

$+4.94 \times 10^{-17} N$
$2.56 \times 10^{-17} N$

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Video Transcript

we begin this question by calculating what is the Net force that acts on the electron and how can you do that? Well, remember that from Newton's second blow, the net force is given by the massed finds declaration. We know the mass of the electron, the mask off letter. That is the question 9.7. I'm stand to minus 30 world kilograms. Now we have to get her mind. What is the exploration and how can we do that? We'll take a look at the data, so the record goes from 5.4 times 10 to 15 meters per second, 22.1 time step into six meters per second. Then the variation in the velocity is 2.1 time stamped realistic minus 5.4. I'm Stan, this is and this happens while the electron was traveling a distance off 0.0 38 meters. So all we knew is no Cassie Anelka. The stents. How can you know what is exploration? We can use your Charlie's equation, which tells us that the final velocity squared is because the initial they lost its were plus two kinds declaration times. It's the displacement. Then we have the following the final velocity Q 0.1 time standing six square is equal to the initial velocity 5.4 I understand square plus true times acceleration times 0.0 38 Then we have to solve this equation for acceleration. In order to do that, we have first to do some things. So we sent this term to the other side to get the following. So we get true 0.1 time stamped with six. We're minors. 5.4 time Stand for the fifth square. Is it close to two times acceleration times 0.0 38. Damn, we had this. We can do the following send both be true on the 0.0 30 exit on the other side. So we got true 0.1 time stamped into six squared minus 5.4. I'm standing Feud queer divided by true kind 0.0 38 Is it close to the acceleration men? They have given this an acceleration off approximately 5.42 time Stand to the 13 meters per second square. So these these declaration now we can go back in complex in that force when that force is. Then it costs 29.11 kind. Stand to minus 31 times five. 40 to understand the 13. Then that force is approximately 4.94. Understand? To minus 17 mu Tums. And this is the answer for the first item. Now, on second. Like them, we have to calculate what is the strength off the force at two. And how can we do that? Well, note that the force that one swinging to the right and the force at two is pointing to the left. Sure, in that force is equal. Stoop at one minus two. The Net Force. We know it's 4.94 Understand? To my 17 the force s one we know a 7.5. Thanks then to the miners. 17. Now, I only have to do to complete the value off, too. We can do that. Like sending his current to the side. His term with the site. So we got to is equal to seven twice. Understand? To my 17 minus 4.9. Before time Stan to mind. 70. And these gives this force too equals true. 2.6. I'm Stan to minus 17 new tops on this. The answer off the second night

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