Compression of spring wrt speed

[brunettegurl]

Homework Statement

A block sliding along a horizontal frictionless surface with speed v collides with a spring and compresses it by 2.34 cm. What will be the compression if the same block collides with the spring at a speed of 4.00v?

Homework Equations

e=0.5mvSUP]2[/SUP] e= 0.5k*x²

The Attempt at a Solution

i thought abt equating the two and solving it in regards but there are too many unknown values to cancel them out...and also to find a way to make a connection btw the given information.
my next thought was to times the given compression by 4 since the speed is also increased but that proved to be wrong..pls. help

 

[Doc Al]

my next thought was to times the given compression by 4 since the speed is also increased but that proved to be wrong

That should be correct. [edit: At first I said it was wrong, but I didn't read it carefully.]

Set up a ratio to verify it.

 

[Pengwuino]

Equate both energies, potential and kinetic for both systems independently. Then divide the equations against each other and see what pops out.

 

[brunettegurl]

ok ...so I'm a little confused abt the divide them against part..so if i do that the k and m would cancel off living (v²+16v²)= (0.0234)²(x²)...does that look right or am i totally off track??

 

[Doc Al]

ok ...so I'm a little confused abt the divide them against part..so if i do that the k and m would cancel off living (v²+16v²)= (0.0234)²(x²)...does that look right or am i totally off track??

I don't quite understand what you did. Yes, the m and k drop out, but you should have v₁²/v₂² = x₁²/x₂² (or equivalent).

(Read my correction to my last post.)

 

[brunettegurl]

ok thanks