Question

#Simple yet not so simple
qn 1)
an ideal spring with spring constant k is hung from the ceiling and a block of mass M is attached to it's lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the string is
a)4Mg/k
b)2Mg/k
c)Mg/k
d)Mg/2k

Answer 1

the answer is 2mg/k

Answer 2

Mg/k?

Answer 3

Good @chand . Would you mind explaining to @goutham1995 ?

Answer 4

sure. when a mass attached to a spring is suddenly released, energy is conserved.
in this case, spring potential energy is equal to the potential energy of spring.
1/2 kx^2 = mgx
and thus x = 2mg/k

Answer 5

- System is conservative (ME is conserved).
- In both situation, mass is at rest, hence KE = 0 and ΔKE = 0
- Gravitational PE is converted in Elastic PE

hence the equation derived by chand.

Answer 6

The common mistake which people make in such question is

F = mg= kx

So x = mg/k

This is the mistake I wanted to point out. :)

Answer 7

lol..thats what i did..but why will it be wrong? if we dont consider energy, how else can we do it?

Answer 8

@Vincent-Lyon.Fr , can you help us here please ??

Answer 9

Energy makes it much easier, but you can also solve it 'the hard way' using SHM equations. I will post this solution, but have no time right now.