Interesting Electric Field and Spring Problemf

[caesius]

Homework Statement

A block having mass m and charge +Q is connected to an insulating spring having constant k. The block lies on a frictionless, insulating horizontal track, and the system is immersed in a uniform electric field of magnitude E as shown in the diagram. 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 (a) assuming that the coefficient of kinetic friction between the block and the surface is mew K.

http://img513.imageshack.us/img513/3959/physprobzm4.png

Homework Equations

a few, F = qE = ma = -kx

The Attempt at a Solution

I'm only starting to attempt part (a), the block has a force QE to the right and a restoring force kx to the left.

So I equated the forces thus: QE = kx and solved for x to obtain x = QE/k.

This isn't the solution for (a), but it is for (b). The solution for (a) is 2QE/k

It's driving me crazy trying to find where the 2 came into calculations. Working backwards from (b) I see that the equilibrium position is half of the maximum expansion. But how so?

 

[cryptoguy]

Right, that's the answer for B because at the equilibrium position, the restoring force of the spring is equal to the electric force. That's why at equilibrium, Fnet is 0 so the acceleration of the block is also zero.

For part A, consider the relationship between the potential energy of the spring at the point of furthest expansion and the work the electric force must do to get the block to that point.

 

[baba89]

I can offer a possible explanation for the discrepancy in your calculations. It is possible that the diagram and problem statement are not accurately representing the scenario. For example, the diagram shows the block being released from the origin (x=0) but the problem statement mentions the block being released when the spring is unstretched (at x=0). These two scenarios could result in different equilibrium positions and maximum expansions.

In addition, the presence of the electric field and charge on the block could also affect the equilibrium position and maximum expansion. It is possible that the electric field is not uniform or that the charge on the block is not accurately represented in the diagram. These factors could also contribute to the discrepancy in your calculations.

As a scientist, it is important to carefully consider all factors and variables in a problem before coming to a conclusion. In this case, it may be helpful to review the problem statement and diagram for any discrepancies or uncertainties, and to double check your calculations to ensure accuracy.