A subway train rounds an unbanked curve at 67 km/h. An unused strap makes an angle of 15 degrees to the vertical. What is the radius of the turn. The book answer is 132 m.
F = ma = mv^2/r
The Attempt at a Solution
A free-body diagram shows a normal force pointing up 75 degrees from the horizontal axis. An mg force points down along the y axis.
Along the x axis N sin 15 degrees = mv^2/r.
r = mv^2/N sin 15 degrees.
Along the y axis N = mg cos 15 degrees.
Substituting, r = mv^2/mg sin 15 degrees/cos 15 degrees = v^2 / g tan 15 degrees
r = (67)^2 km^2/ H^2 / 9.8 m/s^2 / 3600 s^2/ h^2 * 1000 m/km / .268 = 475 m