Why is this force the mgCos while the other is mgSin?

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SUMMARY

The discussion centers on the forces acting on a block placed on a ramp inclined at 60 degrees. The weight of the block is 10 kg, and the coefficient of kinetic friction is 0.3. The key takeaway is that the force component acting down the ramp is represented by mgSin(θ), while the normal force is represented by mgCos(θ). This distinction arises from the geometry of the right triangle formed by the weight vector and the inclined plane, where θ is the angle of inclination.

PREREQUISITES
  • Understanding of basic trigonometry, specifically sine and cosine functions.
  • Knowledge of Newton's laws of motion.
  • Familiarity with the concepts of weight, normal force, and friction.
  • Ability to analyze forces in inclined planes.
NEXT STEPS
  • Study the derivation of forces on inclined planes using free-body diagrams.
  • Learn about the role of friction in motion on inclined surfaces.
  • Explore the effects of varying angles on normal force and acceleration.
  • Investigate the relationship between mass, gravity, and acceleration in different contexts.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the mechanics of forces on inclined planes and the application of trigonometric functions in real-world scenarios.

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Homework Statement


A block is placed on a ramp that is inclined to 60 degrees to the horizon. If the block weighs 10kg and the coefficient of kinetic friction is 0.3, how fast does the block accerlate down the ramp?

Homework Equations


Theta=60 degrees
m=10kg
g=10m/s^2
mu=0.3

The Attempt at a Solution


So far, all I have is the diagram that he gave us in class. I can somewhat tell why we're using the trig functions, but what I'm curious about is why mgsin(theta) is the block sliding down the ramp and mgcos(theta) is the reactionary force of gravity. Why not the other way around?

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Draw the vertical lines from the down edge of mg to the opposite sides of plane and see which angle is ##\theta## in the right triangle that is formed. In this triangle, find each vertical side using trigonometry.
 
upload_2017-2-8_16-36-36.png
This is where theta is to be placed. If you understand why, try to figure it out from there.
 
You can also ask yourself what happens to the normal force as theta approaches zero? Would Sin or Cos do that?
 

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