Two charged balls both with mass mm and charge q are suspended from a thread with length l. They form a small angle θ, with the normal.

Sunday, 12 August 2018

4:03 PM

Machine generated alternative text: Question: Two charged balls both witn mass m and charge q are suspended from a thread with length l. They form a small angle 9, witn the normal. 9 1 Figure 1 Two charge ot equal sign and magnitude q and mass m are connected to a massless string ot length l. When hung trom the same point on the ceiling the üo charges repel each other and are separated by a distance x. Both masses are at an angle 9 from the negative y-axis. part 1) use the small angle approximation to derive an expression tor the angle 9 (in radians) in terms of Co, l, q, m and g. Do not include in your expressiom 9 radians Your last answer was interpreted as follows: 0 part 2) In the case where I = 30.4 cm, q = 1.86"C' and m 48.4 g what angle does the string make with the normal? 9 radians Your last answer was interpreted as follows: 0 part 3) What is the separation, x, in this case? Your last answer was interpreted as follows: 0

 

Machine generated alternative text: Your answer is partially correct Note: Your answers should be correct to 3 significant figures. Feedback tor Part 1) The balls will move to their equilibrium positions when all forces are balanced. In this case mg Figure 1 _ Free-body diagram tor one mass: The mass is not accelerating and tneretore the net force must be zero. The forces on the mass are the tension in the string T, the weight force mg and the electrostatic torce FE. Where FE is the Coulomb force . Redrawing these forces head to tail you can see. 47rE0 X 1 mg 2 Figure 2 Redrawing of Figure 1 of the forces from head to tail. We can write an expression for 9 tor both the force and distance diagram. Forces: tan(9) 47rEox2mg Distance: Sin(9) 21 • using the small angle approximation 9 z tan(9) z sin(9) 9 4mEnx2ma 21

 

Machine generated alternative text: Substituting = 219 into the force expression for 9. 93 Marks for this submissiom 0.00/0.33. This submission attracted a penalty of 0.11 Feedback tor Part 2) You should substitute into the expression derived in the first part: 9 Make sure you put q into C, I into m and m into kg. Marks for this submissiom 0.00/0.33. This submission attracted a penalty of 0.11 Feedback tor Part 3) You have correctly answered this part Marks for this submissiom 0.33/0.33. _g_ which can be typed in as follows: A correct answer A correct answer is 0.562, which can be typed in as follows: e. 562 A correct answer is 34.2, which can be typed in as follows: 34.2 x = 219. 47rEo (218) 2mg 4TE0412mg 1/3 16TE012mg 1/3 167rE012mg

 

 

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