# Archimedes Principle and resonance

1. Apr 10, 2006

### Ukitake Jyuushirou

i got 2 qn , 1 on archimedes principle and the other on resonance

1)The Artic Ice cap is a floating ice mass. If the ice were to melt, how would the depth of the ocean change?

my ans was that it will become deeper but the ans was it will remain the same....why?

2) my understanding is that resonance occur when u do something that matches or exceed the natural frequency of an object rite?

2. Apr 10, 2006

### Hootenanny

Staff Emeritus
This is incorrect. Resonance occurs only when you drive an ocsillating body at its natural frequencey ($f_{0}$). At its natural frequency an ocsillator driven at $f_{0}$ will absorb the maximum amount of energy and therefore will reach it's maximum amplitude. If the system is undamped then the amplitude will tend to infinity. If the occilator is undamped and driven at a frequency of $f<<f_{0}$, then the amplitude of the oscillations will be equal to the amplitude of the driver.

Regards
-Hoot

Last edited: Apr 10, 2006
3. Apr 10, 2006

### Ukitake Jyuushirou

woah...i'm doing introductory physics at university, i dont know some of the terms ur using. wat do u mean by "undamped"? can u explain abit more about natural frequency in layman's term plz

thank :D

4. Apr 10, 2006

### Hootenanny

Staff Emeritus
Undamped basically means that the body (what ever it may be) experences no retarding forces.

The natural freqencey of an object is defined by that object's physical characteristics. If an object is set in motion and not driven by any external force, then it will osciallate at its natural frequency. For example an undriven mass spring system will always ocsillate at a frequencey of;

$$f_{0} = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$$

$f_{0}$ refers to the natural frequency of an osciallting body, fundemental frequency or the first harmonic.

-Hoot

5. Apr 10, 2006

### Mattara

1)The Artic Ice cap is a floating ice mass. If the ice were to melt, how would the depth of the ocean change?

Here is a hint:

If a boat had a rock on it with a mass of 1 ton and 1 $$m^3$$ was in a lake, and suddently the rock got pushed into the lake. The water level would drop.

Volume on boat $$mg=\rho gh$$
Volume in the lake= 1 $$m^3$$

Try to expand that thinking :)

6. Apr 11, 2006

### Ukitake Jyuushirou

if using archimedes principle, the volume of water displaced is = to the volume of the rock. are u saying that if ice cap were to melt slowly then there wouldnt be a change in depth?

7. Apr 11, 2006

### Staff: Mentor

ice cube in a glass of water

Think of the artic ice cap as an ice cube floating in a glass of water. If the ice cube melts, does the water level rise? (Hint: How much water is displaced by the ice cube? When the ice cube melts, how much water is created?)

8. Apr 12, 2006

### Ukitake Jyuushirou

would it be safe to assume that the ice cube itself the mass is made up of water and thus the water displaced is = to its own mass so no change in the sea level?

if thats the case why are global warming scientists harping about melting ice cap?

9. Apr 12, 2006

### Hootenanny

Staff Emeritus
Ice is less dense that water, that's why it floats.

10. Apr 12, 2006

### Staff: Mentor

Exactly.

While the melting of floating ice will not affect sea level, most of the world's ice is grounded.

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