Determine the force involving static coefficient

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SUMMARY

The discussion focuses on calculating the force P required to keep a 200 kg block stationary on an inclined plane with a static coefficient of friction (Us) of 0.5. The correct force P to prevent the block from moving down the incline is determined to be 560.4 N. Two incorrect calculations were presented: one yielding 1028 N and another 665.5 N, both of which failed to account for the correct balance of forces acting on the block. The discussion emphasizes the importance of accurately applying the equations of motion and friction in static scenarios.

PREREQUISITES
  • Understanding of static friction and its coefficient (Us = 0.5)
  • Knowledge of free body diagrams and force balance equations
  • Familiarity with trigonometric functions in physics (sine and cosine)
  • Basic principles of mechanics involving inclined planes
NEXT STEPS
  • Review the derivation of force balance equations for inclined planes
  • Study the effects of varying angles on static friction and force calculations
  • Learn about the implications of different coefficients of friction in static scenarios
  • Explore advanced mechanics topics such as dynamic friction and motion analysis
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and static equilibrium, as well as educators seeking to clarify concepts related to friction and inclined planes.

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Homework Statement


A force P acts as shown on a 200kg block placed on an inclined plane. The static coefficient of friction between the block and plane are Us= 0.5 . Determine the force of P to ensure he block is in the verge of moving down. The ans given is P = 560.4 N
i have done in 2 ways , but my ans is incorrect ... why am i wrong ?

Homework Equations

The Attempt at a Solution


[/B]
1. ) P cos 20 = Fs

Pcos20 =0.5x9.81x200xcos10

P= 1028N

2. ) Wsin10 + P cos20 = 0.5x9.81x200xcos10

Pcos20 = 0.5x9.81x200xcos10 - Wsin10

Pcos20 = 0.5x9.81x200xcos10 – 200x9.81 sin10

P= 665.5N
 

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What about the maximum friction if P were at 90 degrees instead of 20 ?
 
Go through the standard procedure:
Draw the free body diagram of the block. List the forces with horizontal components, write out expressions for their values and the force balance equation. Then do the same for vertical components.
 

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