Understanding Friction on Slopes: Choosing Between Cos and Sine Components

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SUMMARY

This discussion clarifies the resolution of forces acting on a body placed on an incline. When analyzing the gravitational force (mg), the component perpendicular to the slope is represented by the cosine function, while the component parallel to the slope is represented by the sine function. It is crucial to note that the angle of the incline is measured with respect to the y-axis, not the x-axis, which reverses the typical application of trigonometric functions. Understanding this distinction is essential for accurately calculating forces on slopes.

PREREQUISITES
  • Understanding of basic trigonometric functions (sine and cosine)
  • Familiarity with vector resolution in physics
  • Knowledge of gravitational force and its components
  • Ability to interpret angles in relation to axes
NEXT STEPS
  • Study the concept of vector resolution in inclined planes
  • Learn about the role of gravitational force in motion on slopes
  • Explore the application of trigonometric functions in physics problems
  • Review examples of force diagrams for inclined planes
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone seeking to understand the dynamics of objects on slopes will benefit from this discussion.

Shovna
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The question is quite simple by i dnt seem to be getting it..
When a body is placed in a slope.
force mg is resolved into rectangular components..
the one perpendicular to the slope is taken as cos component n the one parallel is taken as sine component.
I don't understand whisch one to take as cos and which one as sine..generally x-axis is cos n y-axis is sine bt m unable to make out in a figure that which ione to take as x-axis n which one as y-axis??


pleasez help
 
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When you want the x & y components of a vector F and the vector's angle is given with respect to the x-axis, then the x-component will be Fcosθ.

But when resolving weight into components parallel (usually called the x-axis) and perpendicular (y-axis) to the incline, realize that the angle of the incline is the angle that the weight makes with the y-axis, not the x-axis. So the trig functions end up getting reversed.

Read this: http://www.physicsclassroom.com/Class/vectors/u3l3e.cfm"
 
Last edited by a moderator:
your F_g fully does not constrabute to friction... becasue the y- component is driving the object down.. or making it stationary
 

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