Does Ramp Steepness Affect Sphere's Descent Time?

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SUMMARY

The discussion centers on the physics of a sphere rolling down a frictionless ramp compared to a block sliding down the same ramp. It concludes that while the gravitational force remains constant due to equal heights, the time taken for the sphere to descend is affected by the steepness of the ramp. Specifically, a less steep incline results in a longer descent time for the sphere due to the reduced component of gravitational force acting along the slope. This relationship is crucial for understanding the dynamics of rolling motion.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with concepts of gravitational force and its components
  • Knowledge of rotational motion and moment of inertia
  • Basic principles of kinematics
NEXT STEPS
  • Study the relationship between incline angle and gravitational force components
  • Explore the concept of moment of inertia in rolling objects
  • Learn about energy conservation in rolling motion
  • Investigate the effects of friction on rolling versus sliding motion
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in the mechanics of motion, particularly in understanding the differences between rolling and sliding objects on inclined planes.

Zmuffinz
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Homework Statement



A Block slides down a frictionless ramp and a sphere rolls without sliding down a ramp of the same angle. the block and sphere have the same mass, start at rest from point A and descend through point B

a) Consider the sphere rolling down the incline without sliding. If the roll is now repeated with an incline that is less steep but of the same height as the first incline, is the sphere's time to reach the botton greater than, less than, or the same as perviously? Justify your answer

Homework Equations





The Attempt at a Solution



I think the sphere would take more time in rolling down the ramp than the first time but then if the height is the same the gravitational pull doesn't change so it would be the same? I don't know slightly confused
 
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Consider the component of the gravitational pull acting along the slope. It is this component that is responsible for the sphere rolling down. How is this component related to the steepness of the slope?
 

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