Force of block pushed against wall

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SUMMARY

The discussion focuses on determining the minimum force, P, required to hold a 20 kg block against a vertical surface with a coefficient of friction of 0.2 at an angle of 30°. The equations of motion were established using a force body diagram, leading to the equations N - Psin(30°) = 0 and -Pcos(30°) + mg + μPsin(30°) = 0. The block remains stationary, indicating zero acceleration, which simplifies the calculations for P. The key takeaway is that understanding static friction and the forces acting on the block is essential to solve for P.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Knowledge of static friction and its coefficient
  • Ability to draw and interpret free body diagrams
  • Familiarity with trigonometric functions in physics
NEXT STEPS
  • Calculate the normal force (N) using the equation N = Psin(30°)
  • Explore the implications of static versus kinetic friction in similar problems
  • Review the concept of equilibrium in physics to reinforce understanding of stationary objects
  • Practice solving problems involving forces at angles and friction
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and forces, as well as educators looking for examples of static friction problems in real-world applications.

uph0
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Homework Statement


A block of mass 20 kg is pushed against a vertical surface (see picture). The coefficient of friction, μ, between the surface and the block is 0.2. If θ = 30°, what is the minimum magnitude of P to hold the block still?
8068667509_7a94fd1fa4.jpg


Homework Equations



f = force of friction = μN

The Attempt at a Solution


I drew a force body diagram and got equations for x and y.
x: N - Psinθ = 0
Y: -pcosθ + mg + f = may

N = psinθ
so f = μ psinθ
I put f = μ psinθ into the y equation

so i get
-pcosθ + mg + μpsinθ = may

I'm stuck here. I want to find P but I don't know the acceleration.
 
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The problem states that the block is still, which would mean that ay = ?
 
uph0 said:
I'm stuck here. I want to find P but I don't know the acceleration.
The question asks:
what is the minimum magnitude of P to hold the block still?
Therefore the magnitude of the velocity is...?
The change in velocity is ...?
The acceleration is ...?

Why "minimum"? What kind of friction is this?
 

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