Centripetal force on a curved bridge

In summary, when a car is speeding over a curved surface, it can lose contact with the ground, as seen in high speed chases and rally driving. The textbook provides the equation S-mg=Mv^2/r, which is the equation for centripetal force. However, it is unclear why the resultant force is S-mg since S=0. The weight of the car should be the only relevant force, forcing it back onto the road. The correct equation for this scenario would be mg=mv^2/r, as the weight acts as the centripetal force. It is possible that S represents the upward force of the road on the car, making the equation mg-S=mv^2/r. S would be
  • #1
aurao2003
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Homework Statement



When a car is speeding over a curved surface e.g a bridge, it sometimes loses contact with the ground. We have seen this many times in high speed chases and rally driving.

In this scenario, the textbook wrote this equation:
S-mg =Mv^2/r
The RHS side is obviously the equation for centripeta force (F=Mv^2/r).
But why is the resultant force S-mg since S=0? I thought the only relevant force should be the weight which acts downwards thereby forcing the car back on to the road. Also in the context of the centripetal force, is it not the weight that acts as the centripetal force in this case. Therefore I was thinking the equation should be
mg =mv^2/r.



Homework Equations





The Attempt at a Solution

 
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  • #2
Is S the upward force of the road on the car?
If so, the equation should be mg-S=mv²/r
S will be equal to zero just at the point where the car leaves the road. Then, as you rightly say, the centripetal force is provided purely by the car's weight mg.
I agree the equation you quoted doesn't make sense.
 

FAQ: Centripetal force on a curved bridge

What is centripetal force?

Centripetal force is the force that keeps an object moving in a circular path. It acts towards the center of the circle and is necessary for an object to maintain its circular motion.

How is centripetal force related to a curved bridge?

In the context of a curved bridge, centripetal force is the force that keeps a vehicle, such as a car, moving in a circular path along the bridge. Without this force, the vehicle would continue in a straight line and potentially veer off the bridge.

How is centripetal force calculated on a curved bridge?

The centripetal force on a curved bridge can be calculated using the formula F = m * v^2 / r, where F is the centripetal force, m is the mass of the object, v is the velocity, and r is the radius of the curved path.

What factors affect the centripetal force on a curved bridge?

The centripetal force on a curved bridge is affected by several factors, including the mass of the object, the velocity of the object, and the radius of the curved path. Other factors such as the coefficient of friction between the tires and the bridge, and the banking angle of the bridge can also affect the centripetal force.

How does the centripetal force on a curved bridge impact the safety of vehicles?

The centripetal force on a curved bridge is crucial for the safety of vehicles. If the force is too weak, the vehicle may not be able to maintain its circular path and may run off the bridge. If the force is too strong, it can cause the vehicle to lose traction and potentially cause an accident. Therefore, understanding and calculating the centripetal force is important for designing safe curved bridges.

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