# Circular motion of a subway train

## Homework Statement

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

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Mentor
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.
Good.

Along the y axis N = mg cos 15 degrees.
You mean: N cos 15 degrees = mg

Substituting, r = mv^2/mg sin 15 degrees/cos 15 degrees = v^2 / g tan 15 degrees
Good.

r = (67)^2 km^2/ H^2 / 9.8 m/s^2 / 3600 s^2/ h^2 * 1000 m/km / .268 = 475 m
First convert 67 km/h to m/s.