Deriving an equation through a free body diagram

Click For Summary
SUMMARY

The discussion focuses on deriving the equation Tan(θ) = static friction on an inclined plane using a free body diagram. Participants emphasize the importance of visualizing forces through a free body diagram to understand the relationship between the angle of inclination and the forces acting on an object. The equation tan(θ) ≤ μ_s, where μ_s represents the coefficient of static friction, is highlighted as a critical aspect of the solution, noting that the friction force can be less than its maximum value, necessitating the use of an inequality.

PREREQUISITES
  • Understanding of Free Body Diagrams
  • Knowledge of static friction and its coefficient (μ_s)
  • Familiarity with trigonometric functions, specifically tangent
  • Basic principles of forces on inclined planes
NEXT STEPS
  • Study the derivation of forces on inclined planes using Free Body Diagrams
  • Learn about the coefficient of static friction and its applications
  • Explore trigonometric identities and their relevance in physics problems
  • Investigate the conditions under which frictional forces act on objects
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and forces, as well as educators looking to enhance their teaching of static friction and inclined planes.

xgdoyo
Messages
2
Reaction score
0

Homework Statement


Use a Free body diagram to show that :Tanθ=static friction, on an incline plane


Homework Equations



FF/FN= coeficiant of friction

The Attempt at a Solution


I know I must get an angle to have a tan of the Force of friction and a Normal force, but I don't understant why i need the the angle
 
Physics news on Phys.org
You should draw out the free body diagram (since that's what the question asks) and that's usually the best way to go about solving these kinds of questions anyway.

What was the actual question? It would make more sense if it asked you to show that:
[tex]tan(\theta) \leq \mu_s[/tex]
(where [itex]\mu_s[/itex] is the coefficient of static friction). And remember that the friction force can be less than its maximum possible value, which is why there is an inequality sign.
 

Similar threads

Replies
4
Views
1K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 14 ·
Replies
14
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
9
Views
2K
  • · Replies 7 ·
Replies
7
Views
4K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
9
Views
2K