an-object-of-mass-m-is-traveling-at-constant-speed-v-in-a-circular-path-of-radius-r-how-much-work-is

Question

An object of mass $m$ is traveling at constant speed $v$ in a circular path of radius $r .$ How much work is done by the centripetal force during one-half of a revolution?
(A) $\pi m v^{2}$
(B) 0
(C) $\pi m v^{2} r$
(D) 2$\pi m v^{2} r$

Yaqub Khan · Accepted Answer

in this problem, we want to find work done by a centripetal force doing one half revolution as we can. Wild work done by centrifugal force equals toe judging kinetic energy off object s object is winning with constant See Pete so kinetic energy off object we lost to be constant These users church in kinetic energy of object equal toe zero. So we can say that work done by centripetal force will be called toe zero. We can also explain this as work done by a centripetal force Physical toe centrifugal force dot displacement is in case off circular motion. Centripetal force is always really in what? And each and at each point, we have the angle between with displacement director and force Equal toe 90 degree so we can write well done by. So do better force equal toe So tubular force in tow, Displacement in tow. Sign off 90 degree. This gives us work done by centripetal force Equal toe Jiro. So at each might we have well done by a centripetal force equal toe zero So this users work done by contributor force in one house revolution is also equal toe zero

Ze-Han Lee · Answer

All right, So, uh, in this problem, we know that Ah, the earth is moving along, Uh, the second copy of it around the around the cell. So this is the earth, and this is the South here and from the problem, we know that the mass of the earth is, um, and the potential velocity. So the message them, the tangential velocities read. Okay. And we also know that Ah, the distance from the sound to the earth is ah, are so These are so one to determine the the work down by the centripetal force W C in a year&#x27;s time. So a year means ah, company, period. Right. Just starting from this position and at the same position. So in a year time, actually, Ah, you can You can just ah, start from another direction. Seeing that because things are your time. There&#x27;s ah, we&#x27;ll come back to the original position and velocity actually will not change saying that says the sound. We&#x27;re not to do any work to the ah, tears. All right, so in that sense, we know that a central force centripetal force w c should people to zero. Okay, so we know that ah w c should be smaller than the given choices, which is to see times Ah, the squid time Sam of are all right.

Ze-Han Lee · Answer

So in this problem, we know that. Ah, object. It&#x27;s moving along. That&#x27;s taking a path with the radius are and And the angular velocity is Ah! Ow! Mika Equal to pi over one second. So this is a two pi raid a second. Okay, s so we can determine the central it. Ow! Aah! This is the centripetal Ah, acceleration, which is which has a formula Omega squared Times are Okay, so this gives us full pi squared. Times are so this is the acceleration on this subject.

Abhishek Jana · Answer

So by definition we know that centripetal acceleration A C is equal to velocity squared over the radius. Now if the radius were doubled, the ax elation should be half. And we can see that by the falling way. So let&#x27;s let&#x27;s double the radio. So we have these great over place are it&#x27;s an ivory have to make we if we have to get back the definition off sent Bill Ex elation. We have to money play half on the left as well. So that means we see that this is half off the X elation. So if the radius is double, then the Senate relaxation would be half. So option B seems to be curry.

Averell Hause · Answer

So during uniform circular motion, we have for, ah four phrases which one is true on. And we can say that, uh, right off that is a no work is done. So this is for a couple of reasons. So no work is done, and we can say that one. Um, no work is done because first, in order for work to be done, we have the force Equalling the displacement Co sign off data. Now. That would mean that this, uh, co sign here, the state A has to be zero degrees, which would make this one. However, it&#x27;s not the case in the sense of uniform circular motion given that here, if he force here were too, um, depend on the direction of the centripetal acceleration. We can say that if we were to have this would be pivot and mia a mass with a uniform circular motion undergoing uniform circular motion here would be the acceleration vector, and the velocity vector would always be tangent to the trajectory of the object. And so we can say that Then this angle okay, Fada equals 90 degrees for ah, uniform circular motion. And so, given that we can say again A is the correct answer. No work is going to be done. And of course, no work is being done by the centripetal force. No work is being done by the velocity. Or rather, velocity is not a force, so it can&#x27;t do work. Velocity doesn&#x27;t have the ability and ah, the potential energy uh, there&#x27;s not depend of does not depend on the position of the object within its own trajectory. So again, ah, statement A is the only true statement. No work is being done during uniform circular motion that is thean of the solution. Thank you for watching.

Erin Goldstraw · Answer

good. What? Look at what problem? 65 in chapter 10 there were told that the Mary Gordon and has a mass off 1640 kilogram and a radius of 7.5 meter. And we want Ah, yeah. Thank your velocity. 01 revolution. Okay. Ah, every eight taken, which is equivalent to seeing that will go around and eighth about evolution per second. And so, uh, we can use you get the It&#x27;s a work done. Yeah, pretty good rendered. The many would end to this speech. We can use creation. It turns to tune that. Which is W cook. Huh? Uh tamed their moment of an asher and times the anger. Fricking angler velocity squared. We could write this eyes the energy if I know energy. Minus the initial energy since we start raced the in a show. Thank you. The velocity You see them. We just need to know if I know the last thing. The nature is the It&#x27;s a creation for the and moment of the national and were tortured digit eyes. I felt like a cylinder. So we get the same expression as example 14 which is home to the moment of inertia. Illegal tow, huh? Came to meth claims the ladies land. The last thing we need to do is before substituting. Enter the formula for the work. Done is cancel H. It&#x27;s to convert our angle of altitude at two. And to a radiance per second claimed to do this years. And so revelations Seconds times. Why, thank you. Yeah. So regions, which simply gives us two. Why? What? Eight radiance for a second. And you know you can substitute and it&#x27;s a huh? So at the moment of a national, Uh huh. Again, the math. Which is corn fix for the ladies. Seven point my cleared on and to pie we were h gland. Soon we can well, cliff age giving calculators and we get the answer. Oh, one for two. Thank you, Jews, and then become our own destiny. Neatest 100. No, to get the answer. Uh, one I want to did. They don&#x27;t gel on DDE. And then as And the solution says we could put this into your scientific institution and not just one point for two times 10 24 Jews. Thank you for listening

Problem 17 Easy Difficulty

An object of mass $m$ is traveling at constant speed $v$ in a circular path of radius $r .$ How much work is done by the centripetal force during one-half of a revolution?
(A) $\pi m v^{2}$
(B) 0
(C) $\pi m v^{2} r$
(D) 2$\pi m v^{2} r$

Answer

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