An accelerometer in a control system consists of a 3.94 g object sliding on a ho

Question

An accelerometer in a control system consists of a 3.94 g object sliding on a horizontal rail. A low-mass spring is connected between the object and a flange at one end of the rail. Grease on the rail makes static friction negligible, but rapidly damps out vibrations of the sliding object. When subject to a steady acceleration of 3.2-g, the object must be located 0.320 cm from its equilibrium position. (b) When the object is displaced 0.320 cm from equilibirum, find the spring force on the object.

Explanation / Answer

the acceleration due to gravity is 9.8 m/s^2 so an acceleration of 3.2 g is equals to =3.2*9.8=31.36 m/s^2

usinf F=ma(F= force, m = mass, a = acceleration),  the force acting on the mass is

F=0.00394*31.36=0.12355 N

spring force F=Kx

k=f/x=0.12355/0.0032=38.612 N/m

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