Curvature/centrifugal force problem

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In summary, a passenger is standing on a train that is running smoothly on a curved track at a rate of 50 m/s. The passenger's weight is 10% greater than when the train is at rest. The track is banked so that the force acting on the passenger is normal to the floor of the train. The problem is to find the radius of curvature of the track. The correct answer is 556m. The attempt to solve the problem using centrifugal force was incorrect, as the correct force to consider is the centripetal force acting horizontally towards the center of the curve. This can be found using Newton's First Law in the vertical direction and the centripetal force equation in the horizontal direction. The mistake made
  • #1
TroyWeathers
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Hey everyone,

I am stuck on a problem that seems so very simple, but I can not get the correct answer on this. I would appreciate anyone who would solve this and/or tell me what I am doing wrong. Sometimes I make stupid mistakes. I know it is probably simple, but just hit a wall on this one.

Problem:A train is running smootly on a curved track at the rate of 50 m/s. A passenger standing on a set of scales observes that his weight is 10% greater than when the train is at rest. The track is banked so that the force acting on the passenger is normal to the floor of the train. What is the radius of curvature of the track?

I am told the final correct answer is 556m.

My attempt is this : Centrifugal force = mg

So, since he is 10% more weight than at rest I have: mg + .10mg = mv^2/r. where m = mass, g= acceleration due to gravity, and r= the radius of the track.

1.1mg = mv^2/r. The masses cancel giving 1.1g = v^2/r. Solving for r gives:

r= v^2/1.1g, which gives me 231.9m for r which isn't correct. Where have I went wrong? Thanks for the help!
 
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  • #2
TroyWeathers said:
Hey everyone,

I am stuck on a problem that seems so very simple, but I can not get the correct answer on this. I would appreciate anyone who would solve this and/or tell me what I am doing wrong. Sometimes I make stupid mistakes. I know it is probably simple, but just hit a wall on this one.

Problem:A train is running smootly on a curved track at the rate of 50 m/s. A passenger standing on a set of scales observes that his weight is 10% greater than when the train is at rest. The track is banked so that the force acting on the passenger is normal to the floor of the train. What is the radius of curvature of the track?

I am told the final correct answer is 556m.

My attempt is this : Centrifugal force = mg
This is wrong. What you are looking for is the centripetal force which acts horizontally toward the center of the curve. There are just 2 forces acting on the car, the weight, which acts vertically down, and the normal force (the scale reading), which acts perpendicular to the banked rails.
So, since he is 10% more weight than at rest I have: mg + .10mg = mv^2/r. where m = mass, g= acceleration due to gravity, and r= the radius of the track.

1.1mg = mv^2/r. The masses cancel giving 1.1g = v^2/r. Solving for r gives:

r= v^2/1.1g, which gives me 231.9m for r which isn't correct. Where have I went wrong? Thanks for the help!
It is the horizontal component of the Normal force that provides the centripetal force. You should be able to get that with some trig by using Newton 1 in the vertical y direction, and the centripetal force equation (Newton 2) in the horizontal x direction.
 
  • #3
Thank you very much. I was making it too simple. That's weird because I usually make things way too hard. I will take a look at it and rework it. Thank you again very much.
 

1. What is the "Curvature/centrifugal force problem"?

The "Curvature/centrifugal force problem" is a concept in physics that refers to the apparent curvature of the Earth's surface and the effect of centrifugal force on objects moving along its surface. This problem arises when trying to reconcile the fact that the Earth is round with the perception that it is flat.

2. How does the Earth's curvature affect objects on its surface?

The Earth's curvature causes objects to appear to move in a curved path when traveling along its surface. This is due to the fact that the Earth is round and the path of an object is affected by the curvature of the Earth. This is known as the Coriolis effect.

3. What is the role of centrifugal force in the "Curvature/centrifugal force problem"?

Centrifugal force plays a role in the "Curvature/centrifugal force problem" because it causes objects to appear to move in a straight line instead of a curved path. This is because centrifugal force acts in the opposite direction of the Earth's gravitational pull, causing objects to move away from the center of the Earth and appear to move in a straight line.

4. How is the "Curvature/centrifugal force problem" explained in the field of physics?

In physics, the "Curvature/centrifugal force problem" is explained through the concept of inertial frames of reference. In this concept, objects appear to move in a straight line when viewed from an inertial frame of reference, such as a point on the Earth's surface. However, when viewed from a non-inertial frame of reference, such as a rotating frame, the motion of objects appears to be curved due to the effects of centrifugal force.

5. Can the "Curvature/centrifugal force problem" be solved?

The "Curvature/centrifugal force problem" is not a problem that can be solved as it is a fundamental concept in physics. However, it can be better understood and explained through the use of mathematical models and theories, such as the Coriolis effect and inertial frames of reference.

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