Energy changes of a stretched string

1. Aug 11, 2015

Janiceleong26

1. The problem statement, all variables and given/known data

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

2. Relevant equations
Hooke's Law: F=kx

3. 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?

2. Aug 11, 2015

Qwertywerty

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

3. Aug 11, 2015

Janiceleong26

Spring force is more than the force of gravity .

4. Aug 11, 2015

Qwertywerty

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

5. Aug 11, 2015

Janiceleong26

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

6. Aug 11, 2015

Qwertywerty

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 .

7. Aug 11, 2015

Janiceleong26

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. :)

8. Aug 11, 2015

Qwertywerty

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

9. Aug 11, 2015

Janiceleong26

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

10. Aug 12, 2015

Qwertywerty

11. Aug 13, 2015

OK thanks