Tangential Acceleration Along an Oddly Shaped Road

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SUMMARY

The discussion focuses on calculating the tangential accelerations of three cars (A, B, and C) traveling at 29.0 m/s on a curved road. The participants emphasize the importance of understanding the normal forces acting on each car, particularly how they differ due to the cars' positions on the road. Car A, on a flat surface, experiences a normal force equal to its weight (mg), while Cars B and C, positioned at the bottom and top of a hill respectively, have different normal forces due to centripetal acceleration. The correct application of Newton's second law is crucial for determining the tangential acceleration through the frictional force, which is derived from the normal force.

PREREQUISITES
  • Newton's Second Law of Motion
  • Centripetal acceleration concepts
  • Friction force calculations
  • Understanding of normal force variations on curved surfaces
NEXT STEPS
  • Study the relationship between normal force and friction in curved motion
  • Learn how to calculate centripetal acceleration for objects on curved paths
  • Explore the implications of varying angles on normal forces and friction
  • Practice solving problems involving multiple forces acting on an object
USEFUL FOR

Students studying physics, particularly those focusing on dynamics and motion, as well as educators seeking to clarify concepts related to forces on curved paths.

  • #31
You solve it symbollically.
 
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  • #32
But, you do know gravity, and when that quantity comes into effect, you use it.
 
  • #33
so is this one asking for a numerical or symbolic answer?
 
  • #34
JeYo said:
It tells me that the normal force - the force of gravity = m_car * a_y = 0, yes?
No. The vertical accelerations of cars B and C are not zero. Don't forget centripetal acceleration.

(If the vertical accelerations were zero, then it would make no difference whether the cars were going over a hill or a valley: all three would be the same. But it does make a difference.)
 

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