How Far Can a Greased Watermelon Be Pulled Down an Inclined Plane?

[Jpyhsics]

Homework Statement

As part of an elaborate prank, a well-greased watermelon (m=4.72 kg) is placed on a ramp inclined with angle θ=27.4° with respect to the horizontal. Because of the grease, the coefficients of static and kinetic friction are µs= 0.560 and µk= 0.392 respectively. The watermelon is attached to the wall, parallel to the ramp, by a spring with constant k=175.2 N/m. What is the farthest distance down the ramp that the watermelon can be pulled away from the spring equilibrium and placed at rest on the surface without the spring pulling the watermelon back up the ramp? Express your answer in metres

Homework Equations

F=ma

The Attempt at a Solution

ΣF_x=mgSinθ-kx-μ_smgCosθ

Rearranged to make:
x=(mg(μ_sCosθ-Sinθ))/(-k)
x=-0.00977m

I used the coefficient of static friction, because it was at rest. Does my solution look correct?
I have included an image of my solution as well.

 

[TSny]

Hello.

Does a negative answer for x seem right?

Check to see if you have the correct direction for the friction force.

 

[Jpyhsics]

Hello.

Does a negative answer for x seem right?

Check to see if you have the correct direction for the friction force.

Why would force of friction be towards the right?

 

[TSny]

Why would force of friction be towards the right?

According to the conditions stated in the problem, is the watermelon on the verge of slipping up the slope or slipping down the slope?

 

[Jpyhsics]

According to the conditions stated in the problem, is the watermelon on the verge of slipping up the slope or slipping down the slope?

Slipping up...oh so the friction has to oppose that verge of motion? My revised answer is 0.253m Does that seem right? And thank you so much!

 

[TSny]

Slipping up...oh so the friction has to oppose that verge of motion? My revised answer is 0.253m Does that seem right? And thank you so much!

Looks right to me.