Maximum Compression of Spring on 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

Gravitational Potential Energy = mgh
now i through i figured out gravitational force was the massXacceleration of g but i took
5X9.8 and got 49 or -49 and both were not correct so i couldn't then move on to figure out the Gravitational Potential Energy so i was stuck there.. and i have to figure that out in order to figure out the entire problem and I am stuck.

The Attempt at a Solution

stated up above...

 

[turin]

now i through i figured out gravitational force was the massXacceleration of g but i took
5X9.8 and got 49 or -49 and both were not correct so i couldn't then move on to figure out the Gravitational Potential Energy

Why do you think that this is not correct? This is correct (in MKS).

Give us something more to go on, so that we can help you effectively. What is your plan to solve this problem? What physical principles will you use?

 

[ordirules]

When the particle moves from the top to the spring, it loses potential energy. However, when it loses this energy, the energy must go somewhere. In this problem, they want to know the point of highest compression in the spring. What is the change kinetic energy of the mass at this point? What is the change in potential energy in the spring? Same for gravity? and how would you relate all these together to get an answer?
(there is no friction so you do not need to worry of energy loss through heat)

hint: $$\Delta E_i = \Delta E_f$$