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# A small sphere of mass $m=7.50$ g and charge $q_{1}=32.0 \mathrm{nC}$ is attached to the end of a string and hangs vertically as in Figure $\mathrm{P} 15.4$ A second charge of equal mass and charge $q_{2}=-58.0 \mathrm{nC}$ is located below the first charge a distance $d=2.00 \mathrm{cm}$ below the first chargc as in Figure $\mathrm{P} 15.4$ . (a) Find the tension in the string. (b) If the stringcan withstand a maximum tension of 0.180 $\mathrm{N}$ , what is the smallest value $d$ can have before the string breaks?

## a. 0.115$N$ b. 0.0125$m$

### Discussion

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##### Christina K.

Rutgers, The State University of New Jersey

##### Andy C.

University of Michigan - Ann Arbor

##### Jared E.

University of Winnipeg

### Video Transcript

Hello. Strings like starter for discussion. Suppose Ah, Smile Bowl is hanging Registry. Okay. And other. Another bowl. It's placed at a distance off two centimeter from this port. Let them first and let them second. Okay, not the mask off. Board One is 7.5 grams. Okay. Is hard to to man a problem that is 3 32 in tow. 10 race par minus nine Coolum. Okay, Not a mass of ball too is similar to Marceau Ball one, that is 7.5 grams. But a charge off board to is minus 50. Eggnog, Nakoula, That is minus 58 in tow. 10 race par minus nine Coolum. Okay, No. Initially you have to find out the tension on this string. Basically, a ball is hanky, so tension will create on the stream. And also this is the ball off. Another charge will create an electrostatic force on this, Then due tothis The tension on the string will also in creams. So porter tension on the string will be MGI force due to their muscle, the ball and the electrostatic force that is exerted by a board to onboard one. So m G plus electrostatic force that is force on one. Due to to this will be the total tension on string. In this case, No, By putting all the values that is 7.5 into 10 resp our ministry engages and 9.8 meters per second squared G plus we know that the form love electrostatic force is constant in tow to one up into cute by the strain square. So for this case, oh, distances too sentimental on the value off constant is nine into 10 respond nine and few one will be 32 in tow, Tenders by minus nine and Q two will be 58 in pretend this bar minus nine. Here we only take the magnet use. And this is Jiraporn Jiro two meter hole square plus Geo point Jill Jiro 75 in 29.8. Now, by solving these questions, we will get the approximately equal to 0.115 Newton. Well, this is the tension that is exerted by the ball one due to its mass and exerted by the electrostatic force that is exerted by the ball too. Okay, no support, no support. If the drinking able to hold for maximum tension off Jiro 0.1 it, Jonathan. The ability off string toehold for maximum tension Is Joep invented Until now, we have to find out the separation between ball one and ball too, so that this drink will not break or just to break. So the formalize same. The Egypt was toe OMG plus electrostatic force TZ equals minus MGI on it will be okay Q one in Tokyo to buy our square But we have to find our dissipation are okay between ball one and ball too. So it ask where Get to one into coup to B minus I'm G Now we have to put all the values basically, uh, under rule cake Q one Q two upon the minus energy. Okay, now we have to put the values so nine interdependence Part nine into well you a few minutes 32 Nano column that you study to interdependence Par minus nine in tow 58 into tenders par minus nine by the maximum tension is geo 0.1 it Newton minus massing toe gravity the masses Jiro 0.75 kg in tow, 9.8 meter per second squared. Now if we solve hold this value. We will get the final distance off. Jiro 0.1, Jiro five Major Well upto this distance, the string will not break. Okay, well, this is all from me for this video. I hope you will like the video. Thank you.

Other Schools
##### Christina K.

Rutgers, The State University of New Jersey

##### Andy C.

University of Michigan - Ann Arbor

##### Jared E.

University of Winnipeg