In a control system, an accelerometer consists of a 5.10-g object sliding on a c
ID: 1418060 • Letter: I
Question
In a control system, an accelerometer consists of a 5.10-g object sliding on a calibrated horizontal rail. A low-mass spring attaches the object to 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 0.840g, the object should be at a location 0.530 cm away from its equilibrium position. Find the force constant of the spring required for the calibration to be correct. N/m
Explanation / Answer
The acceleration due to gravity is 9.8 m/s^2 so an acceleration of 0.840g is equal to 9.8*0.840 = 8.232 m/s^2
Using F=ma (F= force, m = mass, a = acceleration),
the force acting on the mass is
F = 0.00510 * 8.232 = 0.04198Newtons
The spring constant = force/displacement = 0.04198/0.00530 = 7.920 N/m