Solving AP Physics: Spring Compression Problem

[devolg632104]

Homework Statement

A 20 kg mass released from rest slides down a frictionless plane inclined at an angle of 30 deg with the horizontal and strikes a spring of spring constant K=200 Newtons/meter. Assume that the spring is ideal, that the mass of the spring is negligible, and that mechanical energy is conserved. Use g = 10 m/s^2.

a. Determine the speed of the block just before it hits the spring.
b. Determine the distance the spring has been compressed when the block comes to rest.
c. Determine the distance the spring is compressed when the block reaches maximum speed.

Homework Equations

a. V^2=Vo^2 +2ad
b. PE spring = 1/2kx^2
PE = mgh
KE = 1/2mv^2
PE +KE = PE spring
c. Totally clueless

The Attempt at a Solution

For part a, I found what the force of gravity was in the x direction, divided by the mass, and then found the acceleration. Then I plugged that and the given variables into the kinematic equation

V^2=Vo^2 +2ad

And the answer I got was 7.75 m/s

For part b, I tried Ug+K=Us, but I cannot determine the height so I do not know how to do this.

Thanks for the help!

 

[Doc Al]

For part b, I tried Ug+K=Us, but I cannot determine the height so I do not know how to do this.

The amount of spring compression and the change in height are related by a little trig.