# Introductory physics, energy conservation question

1. Nov 7, 2015

1. The problem statement, all variables and given/known data
A 226g block is pressed against a spring of force constant 1.25kN/m until the block compresses the spring 14.3cm. The spring rests at the bottom of a ramp inclined at 62.5° to the horizontal. Using energy considerations, determine how far up the incline the block moves before it stops if there is no friction between the block and the ramp

EDIT b) and if kinetic friction co eff = 0.46

2. Relevant equations
This is where I am stuck, what equations do I even use?

3. The attempt at a solution
The issue is i dont know which equations i use or how to use them for this question.

DeltaU I believe is one of them which is 1/2 kx^2

2. Nov 7, 2015

### BvU

1. Make a drawing
2. Add some symbols of the kind you met in the subject text (slope $\rightarrow$ angle, spring $\rightarrow$ compression energy -- yes ! $E = 1/2 kx^2$ -- , friction, gravity, )
3. Collect equations connecting those quantities
4. post again !

Good luck !

Last edited: Nov 7, 2015
3. Nov 7, 2015

Thanks, so i actually got the first part, the spring potential energy initially = gravitational energy finally and then i drew and triangle and solved for the hypotenuse.

But for part B) im having issues, Initial Pot spring energy - Final grav pot. energy = (0.46)(1.022 (normal force))d

I have two unknowns, the y in mgy of grav pot energy and displacement
and only one equation!

What do i do here please, Thanks!

4. Nov 7, 2015

### BvU

One thing at the time. For a) you must have used some equations other than $E = 1/2 kx^2$. Can you post your work ?

5. Nov 7, 2015

Sure!

1/2 kx^2 = 12.78J

12.78 = mgy

y= 5.77

5.77/sin62.5 = 6.5m (the displacement answer)

6. Nov 7, 2015

### BvU

OK, so the spring energy is converted into gravitation potential energy to the tune of $E = 1/2 kx^2 + 0 \rightarrow E = 0 + mg\Delta y$. what changes when we look at the difference between a) and b) ?

7. Nov 7, 2015

### BvU

You had that in part a) too, but you managed to connect them with a little trigonometry !

8. Nov 7, 2015