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A small sphere of mass I0 kg is released from rest at height of 15.0 m above the ground level. The sphere experiences constant resistive force (due t0 air resistanc...

Question

A small sphere of mass I0 kg is released from rest at height of 15.0 m above the ground level. The sphere experiences constant resistive force (due t0 air resistance) of magnitude R 10.0 N Calculate the speed ofthe sphere after it has fallen through distance of 5,00 m, (8pts)15.0 mCalculate the speed of the ball just before it hits the gound. (Zpts)

A small sphere of mass I0 kg is released from rest at height of 15.0 m above the ground level. The sphere experiences constant resistive force (due t0 air resistance) of magnitude R 10.0 N Calculate the speed ofthe sphere after it has fallen through distance of 5,00 m, (8pts) 15.0 m Calculate the speed of the ball just before it hits the gound. (Zpts)



Answers

A small sphere with charge $q=5.00 \mu \mathrm{C}$ and mass $0.500 \mathrm{~g}$ is traveling horizontally toward the east at a height of $60.0 \mathrm{~cm}$ above the ground. The sphere has a speed of $2.00 \mathrm{~m} / \mathrm{s}$ as it enters a region of uniform electric field with magnitude $E$. What is $E$ if the sphere has a speed of $5.00 \mathrm{~m} / \mathrm{s}$ just before it strikes the ground?

So to begin this problem, you must take a look at the gravitational force acting on this fear. So we know that gravitational force is equal to f equals M g, which is the mass, the object times, its gravitational acceleration. So if we substitute the key, the mass every given and 9.81 for the gravitational acceleration on Earth, we can compute the force. You can compute the gravitational force on the sphere. So if you do that, we're gonna get five times 10 to the power negative, seventh K, g times 9.1. So if you do that, we're gonna get that The force of gravity gravitational force is equal to 4.9 time sent to the negative six Newton. So now we must calculate the electrical force atmosphere, which is which can be calculated by this equation. So F is equal to the charge times the electric fuel strength. So the electric field off the electric field strength off the sheet. Since we don't know this one that was not given to us, we must calculate it. So to calculate that, let's do that over here. So the electric field is equal to this over to times the primitive ity of free space. So if you plug in the values ever given, you can find that we can find out that this so this so we can find out that this is equal to Since these numbers are all given, we know the surface charge density is given in the question which is equal to eight peka peka Cool Mr Pereira Meter square. So if you do that, that's eight PICO is times 10 to the so it's only let me do that. Here, let me do it over your eight times 10 to the negative 12 since its PICO converted back into columns per meter square over to times a primitive ity of free space, which is 8.85 times tend to the negative 12. So if you compute this, we're getting it that the electric field strength is equal to 0.50 point for by 18 Newtons per cool standard units Always good. So now if you go back into the earth electric electrical force, uh, equation over here on this side, we can now use the electrical fuel strength that we completed over here into this equation. So we know that the charge which has given to us is three micro columns, uh, positive three micro plumes. So it's 10 times negative. 63 times at 10 to the power pack of six times the, uh, the electric few friends that we just calculated, which is using a point for 518 So if you just put that into a calculator, we're gonna get that Hold on. Let me just compute this one real quick. I have not read on this. Let me just make the multiple sign. Very clear. So it's three times sent to the negative. Six times zero point 4518 Excuse us. A value off 1.3 55 or list 15 times 10 to the negative six Newtons. So you know that the net force is in a downward direction. So if you seem that Bicol zero at the sheep so the gravitational potential at that point is equal to mg times y or height, so potential, the potential energy at that point is you equals M g times and I which I don't think we need to write down. So for the electric force work done from moving from moving from point A to B is this or if he work done is equal to work done from the point A to B, he is equal to charge times potential difference a minus bi. So that's the potential difference between the 22 points. So if we isolate for the variable cues to find the potential difference, we get that we can just divide both sides by cute. So if you just do that, you can get rid of this. Came over here. And now we can solve for this potential difference which is equal to sorry. So now we can solve for the potential difference. So here, uh, the K is its initial Kontic energy. Hello himself. So So so at point E to be at the sheet and point B is at the distance. Why from the sheet. So if you take that, this potential difference is equal to electrical few friends at why so then the potential energy is you be sequel to negative e y you like. So now if you apply conservation of energy law, it states that the initial potential energy UK plus the initial kind tick potential energy. The initial kind of energy is equal to the final potential energy plus the final Kontic energy Assuming that mirror, this is taking place in ideal conditions and no energy is lost. So we know that the Cayenne tick energy at the start is equal to zero because it starts at rest. So there is no que in this scenario. So if you saw for Katie by moving the the potential energy at point B to the other side of you can get that you a vine issue be he is equal to the kind tick energy and couldn't be so if he further uh, expand on this expression, we're going to get that potential energy at a which we already discussed was MG times in height. So the mg times Why? Why one minus y two? So this is this is a starting height and this is the final height minus. So the potential energy you be completely electrical so minus each you and it's the same thing. So it's why one minus y two consists the difference. So now if we can just substitute since you already know all the values for these return just substituted straight into the calculator. So if you do that or we can go a step further and simplifying this expression so we can do that by factoring out the common common expressions that you're Why one minus y two since Italian. Both. So if you just factor them out, we're gonna get the M G minus C Cube times. Why one? I asked why to is equal to the kind of dick energy at Point B me to find the Cayenne tick energy to find the velocity. So let's keep going. So we know we're in the right direction. So now if you just substitute the values that we have for MGI, which ISS 4.9 times 10 to the power bi calculated this before. So it's the first one 4.9 times 10 to the power negative six. So this gravitational force that we calculated up here mg negative but isn't negative. Six? Yep, minus e que, which we calculated right here. So it's one point 35 time sent to the negative six times that difference, which is just equal to, uh, 0.4 meters. This is straight from the question. So now if you put this into a calculator. We're gonna get that. Hold on. Let me just do this one real quick since I haven't read on this. So 1.35 times sent to the making of six and all of this is one compliant by 0.4. If you do that, Reagan, get that the kind Take energy at point B is equal to, um one point for two times 10 to the negative six and you guessed it. It's type unit juice. So now that we have the kinds of energy at point B, we can use the other former for kind take energy, which is one half MV squared and solved for the we in this case. So if you isolate all the variables for B, you're gonna get an expression that looks something like this. So two times cayenne tick energy over the mass and just square with that whole thing since area square, Uh, for the key to the velocity in this top expression. So now, since we know all these values are just what they're in so two times one point for two time center negative six over the mass, which is five times into negative. Seven. Double check that. Yep. The message. Five times into the negative. Seven on this whole thing is in a square root to know if you compute this in our calculator, we're gonna get that figure. Get the final answer for the velocity. So it's two times the Kontic energy 1.42 times 10 to the negative six over five times sent to them 10 to the power of negative seven. Hold on. I did not write negative there. So 97. And this is equal to 2.1 2.7 Sorry. 2.7 years per second squared. That's it for this one. Thank you for listening.

So here we are, given information about a large insulating sheet. So let's just say this large insulating. She has such certain positive charges uh distributed uniformly across the surface. Yes, so the electric field of this type of sheet, which can be derived from God's law. The electric field is equivalent to sigma over to ε zero. The sigma in this case, if we converted into S. I. Units would be 8.0 times 10 to the negative 12 columns per meter square. And ε zero is any fundamental constant that we can easily find on the table. So, were initially given information that are, we have essentially a small sphere with mass in charge. So the masses 5.00 times 10. And they give seven kg charge of 7.00 million cools. And we're giving information. It's going to go from 0.400 m 2 0.100 m. So, initially it has a speed of zero m/s. And now we're interested in its final speech. So we have to use energy conservation. So the initial energy is going to be equivalent to the final energy. So there's no kinetic energy initially. So, all the energy will be due to the position due to the electric field. So the potential energy do the electric field would be equivalent to charge times the voltage. While the charge times the voltage is also equivalent to be charged times the electric field times the distance from the infinite uh sheet surface. So let's call this distance one, which would be 0.0.400 m. And we're going to have also a potential energy term for distance to However, now we also have a kinetic energy term. So now we're interested in finding this speed. So the electric field with your first determined as well as we already have information about the charge. And we also have information about the mass of the particle To the charge of seven million collapse. So seven times 10 to the negative six multiplied by the electric field eight times 10 to the negative 12 Times two times 8.85, four times 10 to the -12. Then multiplied by Point .3, which is the difference of the two distances. Mhm. Multiplied by two divided by the mass. Mhm. Mhm. Mhm. Yeah, We can find that the speed as a result is equivalent to 1.95 meters per second. And this gives our final answer.

In this problem on the topic of electric fields, we have a small metal ball which has a mass of four g and a charge of five million columns at a distance of 0.7 m above the ground. In an electric field of 12 newton speculum, which is directed to the east, The ball starts from rest and is then released, and we want to find its velocity after it has moved downward, a vertical distance of 0.3 m. Now, as the four g ball fold, the force of gravity acting on it will cause it to accelerate downwards. At the same time they forced you to electric field excellent ball, causing it to accelerate towards the east, the forces that perpendicular to each other, and we can find each component of the velocity. Now the velocity in the downward direction we can use, we can find using equations of motion. The Y squared is equal to the why not squared plus two G. Time's D. Y. Now the time it takes to reach this velocity T. Is V. Y over G. And the acceleration eastward is calculated using it in 2nd law, F is equal to M. A. Which is the electric force, F E Q E. And so the horizontal component of the speed of the ball is A. X times T. Now the vertical component V. Y is equal to from the equation, the square root of two G. Time's D. Y. Now remember the ball starts from rest of the night, why we're not? Y is equal to zero. The time it takes for the ball to fall 30 cm T is equal to The Square Root of two G do I over G. And the acceleration eastward A. Is QE over em. And so therefore the eastward velocity VX is equal to A. X times T. Which is the acceleration Q times E over em time the time Square root of two times g times dy divided by G. And so this can be simplified as Q Q E over em times the square root of two D. Y over G. And so if we put our values into these calculations, we get the Y component of the velocity of the ball to be The square root of two In 29.81 m/km2 Times 0.3 meters which is Dy And so calculating, we get V. Y to be two point 4-6, m/s and thats vertically downward. And then the X, the X component of the velocity is equal to five times 10 to the minus three columns, which is the charge on the ball, Times 12 Newtons per column Divided by the mass of the ball, 0.00 for kg times the square root of two into zero point three m, Divided by G, which is 9.81 m/km2. So we get the X component the velocity to be three 0.70 96 meters per second eastward, and so the velocity, the total velocity of the ball, in unit vector notation Is 3.71 meters per second along the X had direction plus 2.43 m/s along the Y. Hat direction.

My friends, This is the problem Based on column Slop The force off interaction between the two point charges. Cuban and Kyoto separated apart. Why are distance are in free space? Having the magnitude given by K Cuban Kyoto by our square force may be attractive if you want you to having unlike charge and maybe repulsive if they're having the light church in this problem, it is given a small metal sphere having the small metal sphere off must. 0.15 graham are 1.5 in tow, 10 to the power minus four k g and getting the church minus 23 Nano column that is 23 in tow. 10 to the power minus nine column. It is 10 centimeter directly. Ever. This distance is given 10 centimeter. That is 0.1 m carrying the same charge. You're too is also minus 23 toe 10 to the power minus nine. Cooler on this charge is fixed. We have to find in the part eight magnitude of force between this fear. Have fun to or after what second part, If a party spirit released mhm and begin to fall, what is the magnitude off acceleration at a see it first part force off interaction between one and two will be K you want you to buy are the script he is lying into 10 to the governor. Nine. Cuban is 23 in tow, 10 to the power minus nine and the separation between them is quite 1 m the on solving it force off interaction between them. You will get 4.76 and tow 10 to the power off minus four Newton Second part net force on uppers Fair will be Have fun to minus. I am to G on This force will be equal toe mars into acceleration, so it will be happen to minus mg upon him. Now substitute the value Electricity forces 4.76 and tow tend to the par minus four. Moss is given white 15 in tow, 10 to the power minus three. Newton G is 9.8, divided by 0.15 in tow, 10 to the Power Ministry, so acceleration you will get 6.6 m per second squared negative. It means it will accelerate downward. That's so thanks for watching it


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