Mass with a Charge in side an electric field

[shinobi12]

Homework Statement

A block having mass m and charge +Q is connected to an insulating
spring having force constant k. The block lies on a frictionless, insulating horizontal track, and the system is immersed in a uniform electric field of magnitude E
The block is released from rest at a moment when the spring is unstretched (that is, when 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) What if? Repeat part a, assuming now that there is friction between the block and track. Take mew sub k as the relevant coe¢ cient of kinetic friction.

Homework Equations

The Attempt at a Solution

Not sure how to tackle this problem.

 

[gabbagabbahey]

Since your not told anything about whether the block is an insulator or conductor or the dimensions of the block or how the charge distributes itself through the block; the best you are going to be able to do is to assume it can be effectively treated as a point charge with mass $m$ and charge $Q$...What is the electric force on such a charge when it is put in an electric field $\vec{E}\hat{x}$? (I assume that the field is in the x-direction here?)...What other forces are being exerted on the charge?

 

[baba89]

I would start by drawing a free body diagram of the block and identifying all the forces acting on it. The forces would include the electric force, the spring force, and the force of gravity. Since the block is initially at rest, the net force on it must be zero. From there, I would use Newton's second law to find the acceleration of the block and then use the equations for simple harmonic motion to find the maximum amount the spring expands and the equilibrium position of the block. I would also need to take into account the friction force if it is present. To determine the period, I would use the equation T = 2π√(m/k), where m is the mass of the block and k is the spring constant.