Okay, find the maximum elongation. Block is released from rest, block is released from rest
and the spring is at its natural length. Spring is at its natural length. Class, let us discuss one
thing. It was released with zero initial velocity. When will there be maximum elongation?
When it will stop moving. You should understand that the block will move and maximum
elongation means no further elongation. That means block has stopped and will come back.
And during that process this block goes down x distance and this spring gets elongated by x
amount. This problem is spring based, that is why we have to apply energy analysis. So, I will
take this as initial and this as final. Block is moving in vertical plane. Means we have to count
gravitational potential energy. So, let’s take this as a zero potential energy reference line and
in between 1 and 2, I will apply initial kinetic energy, initial potential energy and initial spring
potential energy, all three are zero because in which condition was the spring in the
beginning, rest, natural length. Final kinetic energy zero, final potential energy will it be mg
by, sorry, minus mg x, yes, and what is spring potential energy? K by 2 x square, because if
this goes down then our spring will be elongated, yes or no. So, x is equal to 2mg by k. How
many of you did it right? Now, we will mix the previous example with this example. We will
do one thing, we will search for a special position, such a position where this block has come
down x naught. And this is the position where the weight is applied on this block and the
spring force which is applied on top both are equal. We are assuming that zero force
condition is, you can call it as equilibrium condition, it arrives, when your block comes down
x naught distance, then mg is equal to x naught that means what will the value of x naught
be? Mg by K, right, that means x naught is the elongation at which the force on the block is
zero. What is x naught? Elongation for zero force. Ask, if you have any doubt. We just
assumed that x naught is the elongation because we thought in between force may be zero,
we don’t know and now there is x naught and this is clear also, see this value and see this
value, isn’t it double. Suppose, if I say maximum elongation is there that is 2 times zero force
elongation. Tell me, if it will work or not, we saw this in the previous example. See, last class
last example very carefully. What will be the elongation of zero force? See, last to last
example, F by K and how much is the maximum? Isn’t it, class, this funda is working. Now,
we will see what is happening in this funda basically.
See, there are two forces on the block. One is mg and other is spring force, right. When
value of elongation is less than x naught, that means the block is in this domain. If block is in
this domain, then you will see mg is greater than spring force. So, when does mg becomes
equal to spring force when the value of x is x naught. If value of x is less than x naught, then
mg will be greater than spring force, yes or no. Means where will be the resultant force
applied – Downward direction. And velocity is also down and even acceleration is also down.
Means the speed of our block is increasing, yes or no. That means in this region velocity is
downwards and acceleration is also downwards, so velocity will keep on increasing, okay.
The point has crossed this block and has come in this region. So, in this condition what will
happen? The value of elongation will be more than x naught. See, this value of kx is more
than kx naught. And kx naught is equal to mg, yes or no. That means this time the spring
force value will be greater than mg. If the value of spring force is greater than mg, then the
resultant force acting on the block will act in upward direction. Velocity downward,
acceleration upward, now the block will (8:40). What happens actually, in this question also,
the answer didn’t come as mg by k. In this the answer is 2mg by k because when force is
zero in that condition the force doesn’t stop, before that the block is getting accelerated and
accelerated.