In a control system, an accelerometer consists of a 4.70-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 0.800g, the object should be at a location 0.500 cm away from its equilibrium position. find the force constant of the spring required for the calibration to be correct.

7.37 N/m

Explanation:

Given:

Mass of the object = 4.70 g = 0.0047 kg

acceleration = 0.800 g = 0.800 × 9.81 = 7.848 m/s²

Displacement = 0.500 cm = 0.005 m

Now,

Force by the object = Mass × Acceleration

= 0.0047 × 7.848

= 0.0368856 N

and,

Force by the spring = kx

where, x is the displacement

k is the spring constant

thus,

0.0368856 = k × 0.005

or

k = 7.37 N/m

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