A small sphere is hung by a string from the ceiling of a van. When the van is st

Question

A small sphere is hung by a string from the ceiling of a van. When the van is stationary, the sphere hangs vertically. However, when the van accelerates, the sphere swings backward so that the string makes an angle of with respect to the vertical. Find the acceleration of the van when = 10.6°. A small sphere is hung by a string from the ceiling of a van. When the van is stationary, the sphere hangs vertically. However, when the van accelerates, the sphere swings backward so that the string makes an angle of with respect to the vertical. Find the acceleration of the van when = 10.6°.

Explanation / Answer

given that the string is vertical when the van is stationary
so when the van moves
let acceleration of van be a, mas sof bob be m
then tension in the string be T
angle of string wrt vertical be theta
then from force balance
Tcos(theta) = mg
Tsin(theta) = ma
hence
tan(theta) = a/g
a = g*tan(theta)

now given
theta = 10.6 deg
so a = 9.81*tan(10.6) = 1.835 m/s/s

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