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

In summary, the conversation discusses solving for the maximum distance a well-greased watermelon can be pulled down a ramp without the spring pulling it back up, using the equations F=ma and ΣFx=mgSinθ-kx-μsmgCosθ. The solution is calculated to be 0.253m, taking into account the direction of the friction force opposing the watermelon's potential upward motion on the ramp.
  • #1
Jpyhsics
84
2

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


ΣFx=mgSinθ-kx-μsmgCosθ

Rearranged to make:
x=(mg(μsCosθ-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.
 

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  • #2
Hello.

Does a negative answer for x seem right?

Check to see if you have the correct direction for the friction force.
 
  • #3
TSny said:
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?
 
  • #4
Jpyhsics said:
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?
 
  • #5
TSny said:
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!
 
  • #6
Jpyhsics said:
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.
 

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

1. How does the angle of the inclined plane affect the spring's behavior?

The angle of the inclined plane affects the spring's behavior by changing the force of gravity acting on the mass attached to the spring. As the angle increases, the force of gravity pulling the mass down the plane also increases, causing the spring to stretch further.

2. What is the relationship between the spring constant and the displacement of the spring on an inclined plane?

The spring constant, which is a measure of the stiffness of the spring, determines how much the spring will stretch or compress for a given amount of force. As the displacement of the spring increases on an inclined plane, the spring constant remains the same.

3. How does the mass of the object attached to the spring affect its motion on an inclined plane?

The mass of the object attached to the spring affects its motion on an inclined plane by changing the gravitational force acting on the system. A heavier object will experience a greater force of gravity and will stretch the spring further than a lighter object.

4. What is the significance of the equilibrium position on an inclined plane?

The equilibrium position on an inclined plane is where the force of gravity pulling the mass down the plane is balanced by the force of the spring pulling the mass up the plane. At this point, the spring is neither stretched nor compressed and the object remains at rest.

5. Can the spring's behavior on an inclined plane be described by Hooke's Law?

Yes, the spring's behavior on an inclined plane can be described by Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement from its equilibrium position. As long as the spring is not stretched beyond its elastic limit, Hooke's Law can accurately describe its behavior on an inclined plane.

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