Physics Problem ( Inclined plane and friction)

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SUMMARY

The discussion focuses on calculating the minimum force required to prevent an 80N loaded penguin sled from sliding down a 20-degree inclined plane, considering static friction with a coefficient of 0.25. The user seeks clarification on how to mathematically derive this force using free body diagrams and force balance equations. The solution involves analyzing forces along the x and y axes, ensuring equilibrium by equating the net forces to zero.

PREREQUISITES
  • Understanding of inclined planes and forces
  • Knowledge of static and kinetic friction coefficients
  • Ability to draw and interpret free body diagrams
  • Familiarity with Newton's laws of motion
NEXT STEPS
  • Study the calculation of forces on inclined planes using static friction
  • Learn how to apply Newton's laws to solve equilibrium problems
  • Explore the concept of free body diagrams in physics
  • Investigate the differences between static and kinetic friction in practical applications
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This discussion is beneficial for physics students, educators, and anyone interested in understanding the mechanics of inclined planes and frictional forces in real-world scenarios.

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Homework Statement


A loaded penguin sled weighing 80N rests on an inclined plane 20 degrees to the horizontal. Between the sled and the plane, the coefficient of static friction is .25, and the coefficient of kinetic friction is .15.



Homework Equations


(a) What is the least magnitude of force parallel to the plane, that will prevent the sled from sliding down the plane? More specifically, how do I solve for this force? I draw a free body diagram to set up the problem visually, but I just don't know how to mathematically make sense of it. Thank you.



The Attempt at a Solution

 
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analyze the forces about x, and y axes, and since the penguin will stay at rest so it is in balance, so equate all forces with zero :)
hope it helps
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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