Energy changes of a stretched string

[Janiceleong26]

Homework Statement

This is the answer :

For part d) of this question, I don't understand "stretching/extension reduces and velocity increases/height increases" .

Homework Equations

Hooke's Law: F=kx

The Attempt at a Solution

Ok, so if extension is reduce, then force reduces too. Then how does a decrease in force causes the velocity and height to increase? Does it have something to do with the principle of conservation of energy, where a gain in kinetic energy equals to a lose in gravitational potential energy?

 

[Qwertywerty]

At a point lower than R , how does spring force compare to force of gravity ?

 

[Janiceleong26]

At a point lower than R , how does spring force compare to force of gravity ?

Spring force is more than the force of gravity .

 

[Qwertywerty]

Spring force is more than the force of gravity .

So as long as mass is below R , acceleration is ( +ve or -ve ) ? And therefore velocity will always what ?

 

[Janiceleong26]

So as long as mass is below R , acceleration is ( +ve or -ve ) ? And therefore velocity will always what ?

Positive..? I'm not sure.. Therefore, velocity will increase?

 

[Qwertywerty]

Positive..? I'm not sure.. Therefore, velocity will increase?

Yes . ( kx - mg = ma ) , kx > mg .

Now , a = dv/dt . As a is always positive till before R , dv is always +ve , and hence velocity will increase till R .

Hope this helps .

 

[Janiceleong26]

Yes . ( kx - mg = ma ) , kx > mg .

Now , a = dv/dt . As a is always positive till before R , dv is always +ve , and hence velocity will increase till R .

Hope this helps .

But how do you know that a is always +ve till before R? And why height increases? Does it got to do with 1/2 mv^2=mgh (gain in kinetic energy=lost in gravitational potential energy) ? And thanks by the way. :)

 

[Qwertywerty]

But how do you know that the a is always +ve till before R?

I thought we agreed that -

( kx - mg = ma ) , kx > mg .

And why height increases?

It rises because acceleration is upwards . And that's pretty much the only reason .

 

[Janiceleong26]

I thought we agreed that -It rises because acceleration is upwards . And that's pretty much the only reason .

Yeah, I agreed to that one. But the mark scheme also states that the height increases as well. Why?

 

[Qwertywerty]

Yeah, I agreed to that one. But the mark scheme also states that the height increases as well. Why?

It rises because acceleration is upwards . And that's pretty much the only reason .

 

[Janiceleong26]

OK thanks