The discussion centers on calculating the maximum speed a car can achieve while crossing a hump-backed bridge, modeled as a circular arc with a radius of 35 meters. The key equation used is the centripetal force equation, F = m v²/r, where the normal force becomes zero at the point of losing contact with the bridge. Participants clarify that at this critical point, the centripetal force equals the weight of the car, leading to the conclusion that the maximum speed can be derived from the equation v² = g * r, where g is the acceleration due to gravity.
PREREQUISITESStudents studying physics, particularly those focusing on mechanics, as well as educators seeking to enhance their understanding of centripetal force and its applications in real-world scenarios.
You're supposed to find the speed!Ch3m_ said:I've tried using the equation above but no speed, angular velocity or mass is given.
Do a force analysis of the car as it tops the bridge. Hint: What force tells you when the car is just about to leave contact with the ground?Ch3m_ said:Am I missing something?
Doc Al said:Do a force analysis of the car as it tops the bridge. Hint: What force tells you when the car is just about to leave contact with the ground?
Yes, the normal force that the bridge exerts on the car. What will its value be when the car is barely making contact with the road? What will ΣF be in that case?Ch3m_ said:The reaction force..?
Doc Al said:Yes, the normal force that the bridge exerts on the car. What will its value be when the car is barely making contact with the road? What will ΣF be in that case?
You are making a false assumption. Start from scratch:Ch3m_ said:It must be greater than the weight of the car = mg? I don't know how to get an exact value though
You have the normal force acting upwards, the cars weight acting downwards and the centripetal force acting downwards?What are the forces acting on the car at the highest point?
a = v2/r ?If the car is moving at speed v, what is the acceleration of the car?
Weight + centripetal force so mg + (mv2)/r ?haruspex said:If the car went a little bit too fast it would leave the ground (you are told). What would the reaction force be then?
No, centripetal force is not an applied force. It is that component of the resultant force which produces the centripetal acceleration.Ch3m_ said:You have the normal force acting upwards, the cars weight acting downwards and the centripetal force acting downwards?
Yes, that is the normal force whilst in contact with the ground. But if it just on the point of losing contact, what extra does that tell you about the normal force?Ch3m_ said:a = v2/r ?
Weight - centripetal force so mg - (mv2)/r ?
Yes.Ch3m_ said:Wait so is it v2=gr?
Well, it is because the normal force is zero at that point.Ch3m_ said:Thanks, that must mean the normal force = 0 when the car is on the point of losing contact yeah?