Circular motion of a subway train

[Cantworkit]

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.

Homework Equations

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

 

[Doc Al]

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.

 

[Moetasim]

/ .268 = 132 m

I would first commend the student for using the appropriate equations and attempting to solve the problem. However, I would also suggest that they double check their calculations and units to ensure the accuracy of their answer. Additionally, I would point out that the use of degrees in the calculations may not be the most accurate, as angles are typically measured in radians in physics. Finally, I would encourage the student to think about the concept of centripetal force and how it relates to the circular motion of the subway train, as this understanding can help in solving similar problems in the future.