Question

A small sphere hangs from a string attached to the ceiling of a uniformly accelerating train car. It is observed that the string makes an angle of 23 degrees with respect to the vertical. The magnitude of the acceleration of the train car is most nearly

a. 9.0 m/s²
b. 4.2 m/s²
c. 7.5 m/s²
d. 3.8 m/s²
e. 9.8 m/s²

Answer 1

Let T be the tension in the string

T cos 23 = m g vertical component of T

T sin 23 = m a horizontal component of T

a / g = sin 23 / cos 23 = tan 23

a = g tan 23 = 9.80 m/s^2 * .42 = 4.16 m/s^2

b) is the correct answer