# Spring friction physics

freak_boy186

## Homework Statement

A 50 g ice cube can slide without friction up and down a 30 degree slope. The ice cube is pressed against a spring at the bottom of the slope, compressing the spring 10 cm. The spring constant is 25 N/m. When the ice cube is released, what total distance will it travel up the slope before reversing direction?

F = ma
W = Fdx
Ws = -1/2kx^2

## The Attempt at a Solution

Ws = -1/2(25)(.1)^2 = 0.125J
V1 = [2(.125/.5)]^1/2 = .7071 m/s
F = .5(9.8)(sin30) = 2.45N
2.45/.5 = 4.9 m/s^2

(.7071)^2 = 2(4.9)ds
ds = .0510m = 5.1cm

apparently I'm incorrect in my reasoning...

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## Answers and Replies

aim1732

When the spring decompresses there is change in K.E as well as P.E. You have considered only change in K.E. Rather look at the end positions that concern you most - the elastic P.E at maximum compression will be equal to G.P.E when block comes to rest momentarily at highest pt.

freak_boy186

so what is the equation for P.E. then, cause I thought it was -1/2kx^2...

So... EPIC fail... 5g = .05kg

My answer WAS correct, the decimal place was just off by one...

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benhou

apparently I'm incorrect in my reasoning...

I am not sure what you mean by that. But, your solution looks reasonable. There is an easier way to do it though. simply set $$U_{s}=U_{g}$$ without the kinetic energy.

benhou

By the way, 50g=0.05kg, not 0.5kg.

aim1732

Dear freak_boy I wasn't referring to elastic potential energy rather it was gravitational potential energy . That is why your answer was off by a small margin - the change of height you ignored was small. Nonetheless it is important that you do not ignore it. That is why benhou's method is better.