Question

Three identical small Styrofoam balls of mass 1.89 g are suspended from a fixed point by three nonconducting threads, each with a length of 59 cm and negligible mass. At equi- librium the three balls form an equilateral triangle with sides of 30.6 cm.

What is the common charge carried by each ball? The acceleration due to gravity is 9.8 m/s2 and the value of Coulomb’s con- stant is 8.98755 × 109 N · m2/C2 .

1. 0.190953 2. 0.180562

3. 0.131962

4. 0.127213

5. 0.169465

6. 0.265633

7. 0.194387

8. 0.18699

9. 0.215062

10. 0.198498

Answer in units of ?C.

Answer #1

**distance from cornet to centroid l = (s/2)/cos30 =
(30.6/2)/cos30 = 17.7 cm = 0.177 m**

**angle made by the thread with horzontal =
theta**

**costheta = l/L**

**costheta = 17.7/59**

**theta = 72.576**

**net electric force acting on ball Fe =
2*k*q*q*cos30/s^2**

**In equilibrium for the ball**

**along vertical**

**Fnet = 0**

**T*sintheta - m*g = 0**

**T*sintheta = m*g**

**along horizontal**

**Fnet = 0**

**T*costheta - Fe = 0**

**T*costheta = 2*k*q^2*cos30/s^2**

**tantheta = m*g*s^2/(2*k*q^2*cos30)**

**tan72.576 =
1.89*10^-3*9.8*0.306^2/(2*8.98755*10^9*q^2*cos30)**

**q = 0.18699 uC <<<------------ANSWER**

Two identical cork balls, each of mass m, are
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a) Draw a free-body force diagram for one of the two
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b) Write down ∑Fx = max and...

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