Thread: Why do I have to use energy conservation rather than using tension-extesion?

One end A of a light elastic string of natural length a and modulus of elasticity 6mg is fixed at a point on a smooth plane inclined at 30° to the horizontal A small ball B of mass m is attached to the other end of the string. Initially B is held at rest with the string lying along the line of greatest slope of the plane, with B below A and AB =a. The ball is released and comes to instantaneous rest at a point C on the plane.

Okay NOW It says I have to use a loss of GPE = EPE in the markscheme BUT WHY WHY WHY? Why cant I use

$\displaystyle Tension = \frac{\lambda x_{extension}}{x_{original length}}$

as the particle will stay be equilibrium when Tension balances the downward pull right?

T = mgsin30°
$\displaystyle Tension = \frac{\lambda x_{extension}}{x_{original length}} = mgsin30°$

$\displaystyle \frac{6mg x_{extension}}{a} = mgsin30°$
$\displaystyle \frac{6 x_{extension}}{a} = sin30°$
$\displaystyle x_{extension} = \frac{a}{12}$

therefore AC = a+a/12 = 13a/12

which is wrong!

Howcome????

Thanks

Originally Posted by thomas49th

One end A of a light elastic string of natural length a and modulus of elasticity 6mg is fixed at a point on a smooth plane inclined at 30° to the horizontal A small ball B of mass m is attached to the other end of the string. Initially B is held at rest with the string lying along the line of greatest slope of the plane, with B below A and AB =a. The ball is released and comes to instantaneous rest at a point C on the plane.

Okay NOW It says I have to use a loss of GPE = EPE in the markscheme BUT WHY WHY WHY? Why cant I use

$\displaystyle Tension = \frac{\lambda x_{extension}}{x_{original length}}$

as the particle will stay be equilibrium when Tension balances the downward pull right? right, but the position where the particle comes to rest is not the equilibrium position.

T = mgsin30°
$\displaystyle Tension = \frac{\lambda x_{extension}}{x_{original length}} = mgsin30°$

$\displaystyle \frac{6mg x_{extension}}{a} = mgsin30°$
$\displaystyle \frac{6 x_{extension}}{a} = sin30°$
$\displaystyle x_{extension} = \frac{a}{12}$

therefore AC = a+a/12 = 13a/12

which is wrong!

Howcome????

.