An accelerometer consists of a spring of spring constant k = 1.25 N/m and unstre

Question

An accelerometer consists of a spring of spring constant k = 1.25 N/m and unstretched length 0 = 10.0 cm fastened to a frictionless surface by a pivot that allows it to swivel in any direction in a horizontal plane. A 46.0 g mass is attached to the other end of the spring, as shown in Fig. 5-38. The whole system is mounted securely in an automobile. When the vehicle accelerates, the spring provides a force to keep the 46.0 g mass accelerating with the vehicle; by measuring the stretch of the spring, the acceleration can then be determined. To calibrate the accelerometer, circles marked with values of acceleration can be drawn on its frictionless surface.

(a) How far apart should the circles be if each represents an acceleration of 0.200 m/s2 larger than the next smaller circle?
cm
(b) What should be the radius of the circle marked 1.4 m/s2?
cm
(c) How do you read the direction of the car's acceleration from this device?

It is in the direction of the spring force, away from the center of the circles.It is in the direction of the tangential acceleration.    It is in the direction of the spring force, toward the center of the circles.

Explanation / Answer

a) Horizontal force acting on mass is spring force = F =kx = ma ( where a is the acceleration)

x ( stretch) = ma/k

Each increment of acceleration = 0.2 m/s^2

x = (0.046)( 0.2)/1.25 = 0.0073 m apprx ( distance between consecutive circles)

b) x = ma/K = (0.046)(1.4)/1.25 = 0.05152 m = 5.152 cm apprxc

Since i=unstretched circle has radius = 10 cm

so, this circle will have radius = 10 + 5.152 = 15.152 cm apprx

c) If the mass is at rest relative to the car, acceleration is in the direction of the spring force, towards the center of the circles

c)

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