IIT JEE , AIEEE Forum - Physics , Electricity

sulekha_hi

A block of mass m containg a net of positive charge q is placed on a smooth horizontal which terminates in a vertical wall.The distance from the wall is d .A horizontal electric field is towards right is switched on .Assuming elastic collision .find the time period of the resulting oscillatory motion. is it a simplle harmonic motion?

Mr.IITIAN007

I think the answer is under root (8 d m / q E).
We know that s=(1/2)a x t square.So,here d=(1/2) (qxE / m) x t square.
Hence t1=t2=under root ( 2 d m/ qE).
Thus the required time period is
T=t1+t2=2 t1=2 x under root ( 2 d m/ qE)=under root (8 d m / q E).

But dear , the motion is not S.H.M.It is just oscillatory( to and fro).
Please rate me Sulekha if I am correct.

adisahay

Simple. The acceleration of the block will be = a = qE/m.

Since the distance from the wall is d & initial velocity is zero, then the time taken to reach the wall will be = t =

2d/a =

(2md/qE).

Now, since it is an elastic collision, the block will return to the same distance & that too in the same time. Therefore, the time period T = 2t = 2

(2md/qE).

Here I am not very sure as to whether 1 round is taken to be 1 complete oscillation or half oscillation. If is is taken to be half, then T = 4t = 4

(2md/qE), since u said that it is an SHM.

elessar_iitkgp

There are two walls right?? ... One at the point where the block starts?? Assuming it is so ...
Acceleration of the block = qE/m
Time taken for first collision =

(2dm/qE)
Time period, T = 2

(2dm/qE)
But the motion isn't SHM as there is no force directed towards an equilibrium point.

partha

the motion is surely not shm
as accn is qe/m
and d= 1/2*at^2
T=ROOT(2d/a)=root(2dm/qe)
but as the motion is repated again
therefore the time is multiplied by 2
did you get it ??????????

adisahay

Yea ! elessar & partha r right ! i thought on this & now i am sure it's not an SHM. The force is always constant and so is the acceleration.

cvramana

The motion is not S.H.M. as the force is a constant and is not a function of the displacement. Find the acceleration a of the block. And then apply d = a t2 / 2 to find the value of t. Then the time period is 2t.

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