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

A) 3 interactions

B) 2.78 m/s

C) 2.78 m/s

D) 0 m/s

Step-by-step 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 +
`(kq1q2)/(r12) + (kq1q3)/(r13) + (kq2q3)/(r23)`

hence the total interactions is (3)

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

U =
`(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 =
`√(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