Question

A simple accelerometer can be made by suspending a small object from a string attached to a fixed point in an accelerating object - to the ceiling of a passenger car, for example. When there is an acceleration, the object will deflect and the string will make some angle with the vertical. Find the acceleration of the object in terms of the angle the string makes to the vertical.

Answer 1

Step-by-step explanation:

It is a problem of accelerating frame of reference , in which we need to apply pseudo-force on the object . If the accelerating object like car is accelerating the motion of the pendulum has be be observed with respect to car which is accelerating . A pseudo force equal to ma will be applied in a direction opposite to the direction of car's acceleration, on the pendulum . Here m is mass of the pendulum and a is car's acceleration .

If T be the tension of the string which makes an angle of θ with the vertical

T cosθ = mg

Tsinθ = ma

tanθ =
`(a)/(g)`

θ = tan⁻¹ (
`(a)/(g)` )