Physics problem...

[minoupak]

I thought I had the concept down, but I thought wrong....I seem to be missing a step or my algebra is wrong...please someone tell me what I'm doing wrong?

 

A block of mass (m=12kg) is released from rest on a frictionless incline of an angle (30 degrees). Below the block is a spring which can be compressed .02meters by a force of 270N. The block momentarily stops when it compresses the spring by 0.055m. How far does the block move down the inline from its rest position to this stopping point? and the speed of the block just as it touches the spring.

 

Ok since there are only conservative forces, the equation should be

 

Kinetic(f)+Potential Energies(f) = Kinetic energy (i) + Potential Energies (i).

 

I got stuck from the beginning when I was trying to find out the spring rate...which should just be 1/2*k*x^2...equaling 270N when x=0.02. But then I get spring rating of 1350000N! something's wrong there...then I thought maybe 270N was the work, but the numbers are still wrong...please someone help! thanks!

[Jay-qu]

I think you found a few extra zeros somewhere.. k is measured in Newtons per meter, so if it takes 270N just to compress it .02m then it will take 13,500N to compress it one meter.

 

The total energy of the system at any point will be equal to the energy in the spring when it is fully compressed [math]= 0.5(13,500)(.02^2)[/math]

 

So at the point of first impact with the spring, the kinetic energy is equal to the total energy (from above), equate that to: [math]1/2mv^2[/math] and solve for v to get the velocity at impact.

 

likewise when the object is at its starting point all this energy will be in gravitational potential energy, so equating the total energy to: [math]mgh[/math] and solving for h will give the height.