What Is the Maximum Speed a Car Can Travel Over a Hill Without Leaving the Road?

AI Thread Summary
To determine the maximum speed a car can travel over a hill without leaving the road, key factors include the car's mass of 509 kg, the hill's radius of 154 m, a coefficient of static friction of 0.275, and gravitational acceleration of 9.8 m/s². The speed is crucial because it affects the net force required to keep the car on the road; if the speed exceeds a certain threshold, the centripetal force may not be sufficient to counteract gravitational pull. The relationship between speed and force is essential in calculating the maximum velocity. Understanding these dynamics is vital for solving the problem effectively. The discussion emphasizes the need for a clear connection between speed, force, and motion in this scenario.
RoNiN
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I need help! I've tried so many methods but am still coming up blank.

"The same car now travels on a straight track and goes over a hill with radius 154m at the top. What is the maximum speed that the car can go over the hill without leaving the road? (m/s)"

Important Details:
  • Mass = 509 kg
  • Hill Radius = 154m
  • Coefficient of Static Friction = 0.275
  • Gravity = 9.8 m/s²

Looking for Maximum Velocity! Help please
 
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What have you tried that you think is relevant? Why does the speed make any difference? What is it about the motion of this car that makes the speed important? Is there a net force required to make the car travel the way it does? Is there any connection between the speed and the force.
 

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