Question

a pendulum hanging from the ceiling of a train traveling with constant speed deviates 37 ° from the vertical when the train describes a curve of 60 m radius determines the train's rapids

Answer 1

21 m/s

Step-by-step explanation:

There are three forces on the pendulum:

Weight force mg pulling down,

Vertical tension component Tᵧ pulling up,

and horizontal tension component Tₓ pulling towards the center of the curve.

Sum of forces in the y direction:

∑F = ma

Tᵧ − mg = 0

T cos 37° = mg

T = mg / cos 37°

Sum of forces in the centripetal direction:

∑F = ma

Tₓ = mv²/r

T sin 37° = mv²/r

(mg / cos 37°) sin 37° = mv²/r

g tan 37° = v²/r

v = √(gr tan 37°)

v = √(9.8 m/s² × 60 m × tan 37°)

v = 21 m/s