Question

Two 2.0 g plastic buttons each with + 65 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 the left 2.0 g plastic button?
c. What is the final speed of the right 2.0 g plastic button?
d. What is the final speed of the 5.0 g plastic button?

Answer 1

Answer:

A) 3 interactions

B)  2.78 m/s

C)  2.78 m/s

D) 0 m/s

Explanation:

Given Data :

plastic buttons ( 2 ) = 2.0 g each

charge on each plastic buttons = +65 nC

A) The interactions that have potential energy can be expressed as

V net = v1 + v2 + v3

V net = 0 + $\frac{kq1q2}{r12} + \frac{kq1q3}{r13} + \frac{kq2q3}{r23}$

hence the total interactions is (3)

B) The final speed of the left 2.0 g plastic button

U = $\frac{9*10^9* 10^-18}{0.02} [ 65*250 + 65*250 + (65*65)/2 ]$

U = 0.0155 J  

also U = $2( 1/2 mv^2 )$

      U = mv^2 = 0.0155 J

therefore ;  v = $\sqrt{0.0155/(2*10^-3)}$ = 2.78 m/s

C) final speed of the right 2.0 g plastic button = Final speed of the right 2.0 g plastic button

v = 2.78 m/s

D) The final speed of the 5.0 g plastic button

= 0 m/s