How to Find Maximum Compression of a Spring on a Ramp?

[bricker9236]

Homework Statement

A 5 kg block is placed near the top of a frictionless ramp, which makes an angle of 30o degrees to the horizontal. A distance d = 1.3 m away from the block is an unstretched spring with k = 3000 N/m. The block slides down the ramp and compresses the spring. Find the magnitude of the maximum compression of the spring.

Homework Equations

quadratic equation ax+bx-c
h=d+xsintheta
PE=mgh=mg(d+x)sintheta
PE=1/2kx

mg(d+x)sintheta=1/2kx
0=1/2kx+-mg sintheta +-mgd sintheta
ax+bx-c

The Attempt at a Solution

What i did was plug in the numbers into the quadratic equation and i thought that is all that i had to do.. and the answer is still not correct. if someone could please help me out that would be appreciative =)

 

[ehild]

Your formula for PE is wrong. PE=1/2kx².
You have to solve your quadratic equation of form ax²+bx+c=0.

ehild

 

[bricker9236]

I just tried figuring it out once again..

a=1500
b=48.463
c= 63.002


so then i used the quad equation to solve for X


x= -b +- squareroot b2-4ac / 2a

and x comes out to either be

x= .0506461
x= -.0829547

then i put it back into the equation
PE=.5(k)(x)

and i tried both.. one i got around 3 and the other i got around 10

what else am i doing wrong that i can't figure this out?

 

[ehild]

What does it mean "maximum compression of the spring"? And what is "x" for?

ehild