Q. 50

Expert-verifiedFound in: Page 711

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

Two 2.0 g plastic buttons each with +50 nC of charge are placed on a frictionless surface 2.0 cm (measured between centers) on either side of a 5.0 g button charged to +250 nC.

All three are released simultaneously.

a. How many interactions are there that have a potential energy?

b. What is the final speed of each button?

a. The final speed of the two plastic button's charges are +50 nC 2.4m/s

b. The final charge's speed is + 250 nC 0m/s.

The expression of the potential energy in the charge is

Here, Q and q are the charges of the particles.

*K *is constant and* r* is distance.

Let's assume the heavy button is in the middle which is button 2 and in its left the button is 1 and on the right the button is 2.

Thus, there are there types of interactions that are noticed here,

are the potential energies.

Here, are the potential energies in which 1 and 2, 2 and 3, and 1 and 3 are respectively.

The mass in the center is not able to move because of the symmetry but all the masses of the sides move because of the speed *V*.

the conservation energies and the kinetic energy masses are equals to the potential energy in the system which is,

here, are initial and final potential, the proton mass is* m* and K_{i} and K_{f}_{ } are kinetic energies.

on the other hand, the distance between the charges are respectively .

the substitute of 0.20m is for r_{12} and r_{23}, 0.40 is for r_{13} and 50nC is for q_{1} and q_{3}, 250nC for q_{3}, 0.0020 kg for m and for k in this expression,

Therefore, the final speed of two +50nC charged plastic buttons is 2.4 m/s and the final speed of the +250nC charged button is 0 m/s.

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