Electric potential of tiny spheres question

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SUMMARY

The discussion focuses on calculating the electric potential energy and subsequent motion of two charged metal spheres, A and B, each with a charge of 4.50 µC and masses of 3.40 g and 3.90 g, respectively. The electric potential energy (U) is calculated using the formula U = kq²/r, yielding a value of 0.18225 J when the spheres are 1.00 m apart. Upon cutting the connecting string, the acceleration of each sphere can be determined using Newton's First Law, while the final speeds after a long time can be derived from conservation of momentum and energy principles.

PREREQUISITES
  • Understanding of electric potential energy and its calculation using U = kq²/r
  • Familiarity with Newton's laws of motion, particularly Newton's First Law
  • Knowledge of conservation of momentum and energy principles
  • Basic grasp of electrostatics and the behavior of charged particles
NEXT STEPS
  • Study the derivation and application of the formula for electric potential energy in electrostatics
  • Learn about Newton's laws of motion in detail, focusing on applications in particle dynamics
  • Explore conservation laws in physics, specifically conservation of momentum and energy
  • Investigate the behavior of charged particles in electric fields and their interactions
USEFUL FOR

Students studying physics, particularly those focusing on electrostatics and dynamics, as well as educators seeking to clarify concepts related to electric potential energy and motion of charged bodies.

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Homework Statement


Two tiny metal spheres A and B of mass mA = 3.40 g and mB = 3.90 g have equal positive charges q = 4.50 µC. The spheres are connected by a massless nonconducting string of length d = 1.00 m, a distance that is much greater than the radii of the spheres.
(a) What is the electric potential energy of the system?
__J
(b) Suppose you cut the string. At that instant, what is the magnitude of the acceleration of each sphere?
__m/s2 (Sphere A)
__m/s2 (Sphere B)
(c) A long time after you cut the string, what is the speed of each sphere?
__m/s (Sphere A)
__m/s (Sphere B)

Homework Equations



V=U/q
V=-W/q
V=kq/r
U=kq/r^2
K=.5mv^2

The Attempt at a Solution



My teacher told me to use conservation of energy and momentum.

a) U=kq^2/r
U=((9*10^9)(4.50 µ)^2/1
U=.18225 Ji don't understand part B-C
 
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For b), find the force acting on both particles and use Newton's First Law to find the accelerations.

For c), use conservation of momentum and energy. What is the potential energy when the particles are very far away? How are the velocities related? ehild
 

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