A `4.00 kg` block carrying a charge `Q = 50.0muC` is connected to a spring for which k = 100 N/ m. The block lies on a frictionless horizontal track, and the system is immersed in a uniform electric field of magnitude `E = 5.00 xx 10^5 V/m`, directed as shown in figure. If the block is released from rest when the spring is unstretched (at x = 0).

(a) By what maximum amount does the spring expand?
(b) What is the equilibrium position of the block?
(c) Show that the block's motion is simple harmonic and determine its period.
(d) Repeat part (a) if the coefficient of kinetic friction between block and surface is 0.2.

Answer

C, D

Explanation

a. By comparing this problem with spring block system problem suspended vertically.
Here, `mg=-qE=50xx10^-6xx5xx10^5=25N`
`X_max=2mg//K`
Here, `X_max=2qE//K=(2xx25)/100=0.5m`
or `=50cm`
b. Equilibrium position will be at `x=mg//K`
Here, it will be at `x=qE//K=25/100=0.25m`
or `25cm`
c. Force `QE` is contant force, which does not affect the period of oscillation of `SHM`
`:. T=2pisqrt(m/K)=2pisqrt(4/100)`
`=(2pi)/5s=1.26s`
d. `mumg=0.2xx4xx10=8N`
Therefore, here constant force will be
`qE-mumg=25-8=17N=F` (say)
`X_max=(2F)/K=(2xx7)/100`
`=0.34m`