A simple accelerometer is constructed inside a car by suspending an object of ma

Question

A simple accelerometer is constructed inside a car by suspending an object of mass m from a string of length L that is tied to the car's ceiling. As the car accelerates the string–object system makes a constant angle of with the vertical.

(a) Assuming that the string mass is negligible compared with m, derive an expression for the car's acceleration in terms of and show that it is independent of the mass m and the length L. (Use the following as necessary: and g.)

b) Determine the acceleration of the car when = 20.1°.

Explanation / Answer

When the object is suspended by string, there is also a Tension T in addition to mg and psedo force ma,

Balancing force on the object,

in vertical direction:

Tcos theta = mg....eq1

in horizontal:

Tsin theta=ma......eq2

dividing eq2 by eq1

tan theta= a/g

a = g tan theta Answer

hence it is independent of m and L

B) a = g tan20.1degree = 9.8x0.366 = 3.586 m/s2 Answer

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