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the answer is a)gtanO b)4.16 m/s/s please show me how you do it by detail, thank

ID: 1333260 • Letter: T

Question

the answer is

a)gtanO

b)4.16 m/s/s

please show me how you do it by detail, thank you

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 theta 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 theta and show that it is independent of the mass wand the length (b) Determine the acceleration of the car when t = 23.0 degree.

Explanation / Answer


a)

here,

acceleration of car is equal to acceleration of the object

force of horizontal component is,

Fx=ma

T*sin(theta)=m*a -----(1)

and

force of vertical component is,

Fy=mg

T*cos(theta)=m*g ------(2)


from eqn (1) and (2)

(mg*sin(theta))/cos(theta)=m*a


===>

a=g*tan(theta)


b)


if theta =23 degrees,

a=g*tan(theta)

a=9.8*tan(23)

a=4.16 m/sec^2