The charged balloons are in equilibrium with identical positive charges of Q con

Question

The charged balloons are in equilibrium with identical positive charges of Q concentrated at their centers. The rope are massless and rigid i.e ropes do not bend

1. Label all the forces acting on the balloon on the right

2. Draw and label the x and y components of the forces you identified

3. Use coulomb's law and newton's second law to develop an equation for Q as a function of R,L,m, k and g. use no number at this point

4. Use the values given above for R,L,m,K and g to find the value of Q, the charge on one of the balloons

5. Find N the number of electrons on each balloon

6. What is the value of the angle arctan shown on the diagram

her O. SS meter kilogram lo Mb n mete O meter each charge ballo pose Determine charge and number of electrons on The charged balloons are in equilibrium with identical positive charges concentrated at their centers. The rope are massless and rigid i.e ropes do not bend 1. Label all the forces acting on the balloon on the right 2. Draw and label thexand y components of the forces you identified 3. Use coulomb's law and newton's second law to develop an equation for as a function of RLm, k and g. use no number at this point 4. Use the values given above for R,Lm,K and g to find the value of Q, the charge on one of the balloons 5. Find N the number of electrons on each balloon 6. What is the value of the angle arctan shown on the diagram

Explanation / Answer

(3)

from the figure

h = sqrt(L^2-(R/2)^2)

h = (1/2)*sqrt(4L^2-R^2)

tantheta = (R/2)/h

tantheta = R/(2h)

tantheta = R/sqrt(4L^2-R^2)

coulomb's law Fe = k*Q^2/R^2

along vertical

T*costheta = Fg = mg

along horizontal

T*sintheta = Fe

tantheta = Fe/Fg = k*Q^2/(R^2*mg)

R/sqrt(4L^2-R^2) = k*Q^2/(R^2*mg)

Q^2 = R^3*mg/(k*sqrt(4L^2-R^2))

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4)

Q^2 = 1.04^3*7.2*10^-4*9.8/(9*10^9*sqrt((4*0.55^2)-1.04^2))

Q = 1.6*10^-6 C

---------------

5)

number of electrons n = Q/e = 1.6*10^-6 /(1.6*10^-19) = 10^13

-------------------

6)

angle theta = arctan(R/sqrt(4L^2-R^2))

angle = arctan(1.04/(sqrt((4*0.55^2)-1.04^2))) = 71 degrees

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