Acceleration with inclined ramp (Frictionless)

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SUMMARY

The acceleration of a skateboard down a frictionless ramp inclined at 19.5 degrees is calculated using the equation a = g sin(θ), resulting in an acceleration of 3.271 m/s². The confusion arises from the misconception that the formula should be g divided by sin(θ), which would yield an incorrect value exceeding the gravitational constant of 9.81 m/s². The correct interpretation involves understanding that g sin(θ) represents the gravitational component acting along the incline. Visual aids, such as vector diagrams, can clarify this concept effectively.

PREREQUISITES
  • Understanding of basic physics concepts, particularly Newton's laws of motion.
  • Familiarity with trigonometric functions, specifically sine.
  • Knowledge of gravitational acceleration (g = 9.81 m/s²).
  • Ability to interpret vector diagrams in physics.
NEXT STEPS
  • Study the derivation of inclined plane motion equations in classical mechanics.
  • Learn about the role of friction in inclined plane problems.
  • Explore advanced topics in dynamics, such as forces on inclined planes.
  • Review vector decomposition techniques in physics for better understanding of forces.
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in understanding motion on inclined planes without friction.

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1. What is the acceleration of a skateboard down a ramp inclined at 19.5 degrees to the horizontal?

3.271 is the answer.




2. I know g Sin\vartheta is the equation to get it, but I don't get why it isn't g divided by Sin\vartheta



3. In my head I thought the picture was like this:
2wew8bq.jpg


I know this should be something super easy, so please explain. haha
 
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g sin theta gives you the component of the acceleration of gravity along the incline.
g/sin theta would give you a number larger than 9.81m/s^2 which would make absolutely no sense.
 
hp-p00nst3r said:
g sin theta gives you the component of the acceleration of gravity along the incline.
g/sin theta would give you a number larger than 9.81m/s^2 which would make absolutely no sense.

Right, but the first statement still confuses me. Is there a picture you could go by for this?
 
This should help you

http://img145.imageshack.us/img145/6905/accelerationvectorgh9.jpg
 
Last edited by a moderator:
Okay, that totally makes sense now. Thanks! :)
 

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