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A circular road of radius ris banked for a speed v = 40 km/hr. A caro mass attempts to go on the circular road.The friction coefficient between the tyre and the road is negligible.(A) if car turns ai the corect speed of 40 km/hr, the force by the road on the car is greater than mg and mv²/r. explain how?
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A circular road of radius ris banked for a speed v = 40 km/hr. A caro ...
If the car turns at a speed less than 40 km/hr, it will slip down
If the car turns at the correct speed of 40 km/hr, the force by the road on the car is greater than mg as well as greater than mv2/r
This question is part of UPSC exam. View all JEE courses
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A circular road of radius ris banked for a speed v = 40 km/hr. A caro ...
Understanding the Forces on a Banked Circular Road
When a car travels on a banked circular road, several forces come into play. The situation changes when we consider the speed of the car and the banking angle of the road.
Forces Acting on the Car
- Weight of the Car (mg): This force acts downward due to gravity.
- Normal Force (N): This is the force exerted by the road on the car, acting perpendicular to the surface of the banked road.
- Centripetal Force (mv²/r): This force is necessary to keep the car moving in a circular path and is directed towards the center of the circle.
Banking Angle and Speed
- The road is banked at a specific angle θ to allow cars to turn without relying heavily on friction.
- At the correct speed of 40 km/hr, the banking angle enables the normal force to provide the necessary centripetal force while also balancing the weight of the car.
Force Analysis
- When the car travels at the correct speed, the components of the normal force can be resolved into two directions:
- Vertical Component (N cos θ): Balances the weight (mg).
- Horizontal Component (N sin θ): Provides the centripetal force (mv²/r).
- Given that the friction is negligible, the normal force must be greater than the gravitational force to maintain balance and provide sufficient centripetal acceleration.
Conclusion
- At the correct speed, the normal force does indeed exceed both mg and mv²/r because it must account for both the weight of the car and the necessary centripetal acceleration, ensuring the car can navigate the turn safely.
Understanding these forces helps in appreciating the dynamics of vehicles on banked roads, ensuring higher speeds can be maintained without slipping off the path.
When a car travels on a banked circular road, several forces come into play. The situation changes when we consider the speed of the car and the banking angle of the road.
Forces Acting on the Car
- Weight of the Car (mg): This force acts downward due to gravity.
- Normal Force (N): This is the force exerted by the road on the car, acting perpendicular to the surface of the banked road.
- Centripetal Force (mv²/r): This force is necessary to keep the car moving in a circular path and is directed towards the center of the circle.
Banking Angle and Speed
- The road is banked at a specific angle θ to allow cars to turn without relying heavily on friction.
- At the correct speed of 40 km/hr, the banking angle enables the normal force to provide the necessary centripetal force while also balancing the weight of the car.
Force Analysis
- When the car travels at the correct speed, the components of the normal force can be resolved into two directions:
- Vertical Component (N cos θ): Balances the weight (mg).
- Horizontal Component (N sin θ): Provides the centripetal force (mv²/r).
- Given that the friction is negligible, the normal force must be greater than the gravitational force to maintain balance and provide sufficient centripetal acceleration.
Conclusion
- At the correct speed, the normal force does indeed exceed both mg and mv²/r because it must account for both the weight of the car and the necessary centripetal acceleration, ensuring the car can navigate the turn safely.
Understanding these forces helps in appreciating the dynamics of vehicles on banked roads, ensuring higher speeds can be maintained without slipping off the path.
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A circular road of radius ris banked for a speed v = 40 km/hr. A caro mass attempts to go on the circular road.The friction coefficient between the tyre and the road is negligible.(A) if car turns ai the corect speed of 40 km/hr, the force by the road on the car is greater than mg and mv²/r. explain how?
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A circular road of radius ris banked for a speed v = 40 km/hr. A caro mass attempts to go on the circular road.The friction coefficient between the tyre and the road is negligible.(A) if car turns ai the corect speed of 40 km/hr, the force by the road on the car is greater than mg and mv²/r. explain how? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A circular road of radius ris banked for a speed v = 40 km/hr. A caro mass attempts to go on the circular road.The friction coefficient between the tyre and the road is negligible.(A) if car turns ai the corect speed of 40 km/hr, the force by the road on the car is greater than mg and mv²/r. explain how? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular road of radius ris banked for a speed v = 40 km/hr. A caro mass attempts to go on the circular road.The friction coefficient between the tyre and the road is negligible.(A) if car turns ai the corect speed of 40 km/hr, the force by the road on the car is greater than mg and mv²/r. explain how?.
A circular road of radius ris banked for a speed v = 40 km/hr. A caro mass attempts to go on the circular road.The friction coefficient between the tyre and the road is negligible.(A) if car turns ai the corect speed of 40 km/hr, the force by the road on the car is greater than mg and mv²/r. explain how? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A circular road of radius ris banked for a speed v = 40 km/hr. A caro mass attempts to go on the circular road.The friction coefficient between the tyre and the road is negligible.(A) if car turns ai the corect speed of 40 km/hr, the force by the road on the car is greater than mg and mv²/r. explain how? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular road of radius ris banked for a speed v = 40 km/hr. A caro mass attempts to go on the circular road.The friction coefficient between the tyre and the road is negligible.(A) if car turns ai the corect speed of 40 km/hr, the force by the road on the car is greater than mg and mv²/r. explain how?.
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A circular road of radius ris banked for a speed v = 40 km/hr. A caro mass attempts to go on the circular road.The friction coefficient between the tyre and the road is negligible.(A) if car turns ai the corect speed of 40 km/hr, the force by the road on the car is greater than mg and mv²/r. explain how?, a detailed solution for A circular road of radius ris banked for a speed v = 40 km/hr. A caro mass attempts to go on the circular road.The friction coefficient between the tyre and the road is negligible.(A) if car turns ai the corect speed of 40 km/hr, the force by the road on the car is greater than mg and mv²/r. explain how? has been provided alongside types of A circular road of radius ris banked for a speed v = 40 km/hr. A caro mass attempts to go on the circular road.The friction coefficient between the tyre and the road is negligible.(A) if car turns ai the corect speed of 40 km/hr, the force by the road on the car is greater than mg and mv²/r. explain how? theory, EduRev gives you an
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