THE ANSWER IS 25.91. PLEASE SHOW ME HOW TO GET THIS ANSWER. A charge of -7 micro

Question

THE ANSWER IS 25.91. PLEASE SHOW ME HOW TO GET THIS ANSWER.

A charge of -7 micro-coulombs and a mass of 1.4 kg lies on a horizontal surface at rest. Directly 1.1 meters above the charge, is a charge of -9 micro-coulombs. Another charge of +5 micro-coulombs is placed somewhere to the right of the charge on the surface. If the coefficient of static friction is 0.33, what is the minimum distance this third charge can be placed before it begins to move the other charge on the surface (the first charge)? Answer in centimeters.

Explanation / Answer

We calculate the electrical forces and introducing in the equation of the force of friction using Newton's second law

F12 = k q1 q2 / r122    

Data

. q1 = -7 10-6 C                             q2= - 9 10-6 C          r12 = 1.1 m

. q3 = + 5 10-6 C  

      F12 = 9 109   7 10-6   9 10-6 / 1.12             F12 = 468.60 10-3 N

We use Newton's second law

Axis y

N –F12 –W =0       N = F12+ mg               N= 468.60 10-3 + 1.4   10       N= 14.47 N

Note that normal is the reaction to all forces

Axis x

F13 – fr =0        F13=fr                 fr = m N

F13 = k q1 q3 / r132                    F13 = 9 109 7 10-6 5 10-6 / r132

F13 = fr                     9 109 7 10-6 5 10-6 / r132 = 0.33 (14.47)

. r132 =    9 109 7 10-6 5 10-6 / 0.33 (14.47) = 315 10-3 /4.774= 0.06598

. r13 = 0.2569 m = 25.69 cm

Check the exercise twice and this is the result the most important thing to check is the procedure. The difference is in the decimals used.

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