Calculating Train Speed Using Centripetal Force | 15° Angle, 150m Radius

[Slam]

Homework Statement

There is a subway derailed. Radius of an unbanked curve is 150 m. An unused strap hangs at a 15 degrees angle to the vertical just before the accident. Did the train exceed 35 km/h and what speed was it at just before the accident.

Homework Equations

F=ma=m(v^2/r)

The Attempt at a Solution

The angle of the Normal force is 75 degrees counterclockwise to the horizontal axis. The x-component of Force is m(v^2/r)=Ncos75
The y-component of Force is 0=Nsin75-mg
m=(Nsin75)/g Substitute this in for m in the x-component
((Nsin75)/g)(v^2/r)=Ncos75
v^2=g*r*tan75
g=35.28 km/h
r=.150 km
v=4.44 km/h

 

[Orodruin]

You have the wrong numerical value for g. Probably resulting from using the wrong physical dimension. The gravitational acceleration is 9.8 m/s^2, not 9.8 m/s. The unit km/h is a unit of velocity, not of acceleration.

You should note that your equation would not be dimensionally consistent if g had dimension L/T.

 

[rude man]

g=35.28 km/h

This is dimensionally and numerically incorrect..
Work with consistent units: 1km = 1000m
1hr = 3600 sec.
That's why they invented the SI unit system!
Everything else you did looks right.
The answer is way higher than what you came up with.

 

[haruspex]

g=35.28 km/h

As others have noted, your problem is a failure to keep track of units. If you multiply 9.8m/s² by 3.6 (km/h)/(m/s) you get 35.28 km/h/s. Multiplying that by .15 km yields units of km²/h/s, not (km/h)².