Solve Kinematics Problem: Subway Train, Unbanked Curve, 15° Angle

[con31773]

A subway train rounds an unbanked curve at 67km/h. A passenger, hanging onto a strap notices an adjacent strap is unused and makes an angle of 15° to the vertical. What is the radius of the turn?

Relation of sines, opposite and hypotenuse of a right triangle. Opposite length=Hypotenuse*sin(angle)
circular motion equations, such as f=mv$^{2}$/r

First convert the speed into meters per second. 67000m/h=18.61m/s
I recognised that the force causing the angle is centrifugal force, and will be equal in magnitude to the centripetal force. Centrifugal force=mgsin(15)=mv$^{2}$/r (from soccahtoa)
r=v$^{2}$/gsin(15) plug in
r=136.4m, which of course is incorrect.
Any help would be greatly appreciated.

 

[BruceW]

firstly, what direction is the centrifugal force? This should tell you that mgsin(15)=mv²/r is incorrect. Also, there is another real force which acts on the strap.

 

[con31773]

Well the centrifugal force should point in the opposite direction as the centripetal force, which always points to the center of the circle, therefore, it points in the direction the strap has been displaced. Asides from gravity and the force experienced due to the turning effect, I can't think of any other forces present.

 

[BruceW]

the centre of the circle is not in the direction the strap has been displaced. the strap is hanging at an angle, but the circle is horizontal since the motion is only horizontal. The other force is not obvious at first, because the strap is a continuous object. it's mass is distributed over the object. It is probably easier to think of the strap as simply a very light string with a mass at the end of it. what is the other real force acting on that mass (apart from gravity)?

 

[paranormal]

I would first check if all the given values and equations are correct and consistent. Converting the speed into meters per second is correct, and the equation for centrifugal force and centripetal force is also correct. However, the value for the angle should be converted into radians before using it in the equation. 15° is equivalent to 0.26 radians.

Next, I would double check if the direction of the forces is correct. Centripetal force should be directed towards the center of the curve, while centrifugal force is directed away from the center. Therefore, the angle should be used as sin(180-15) or sin(165) in the equation.

Using the corrected value for the angle, the radius of the turn can be calculated as r= 18.61^2 / (9.8*sin(165)) = 73.6 meters.

If this value is still incorrect, I would check for any other external forces that may affect the motion, such as friction or air resistance. If all the values and equations are correct and there are no other external forces, then the given information may not be enough to accurately solve the problem. Further information or clarification may be needed to accurately determine the radius of the turn.