Question

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 u 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 u and show that it is independent of the mass m and the length L.
(b) Determine the acceleration of the car when u 5 23.0°.

Answer 1

(a) g tan u

(b) 4.16 m/s^2

Step-by-step explanation:

(a) Let the acceleration of the car is a.

Due to the psheudo force, the mass moves back.

According to the diagram

tan u = ma / mg

tan u = a / g

a = g tan u

(b) u = 23°

a = g tan 23°

a = 9.8 x tan 23°

a = 4.16 m/s^2

Answer 2

Part a)

`\theta = tan^(-1)(a)/(g)`

so here the angle made by the string is independent of the mass

Part b)

`a = 4.16 m/s^2`

Step-by-step explanation:

Part a)

Let the string makes some angle with the vertical so we have force equation given as

`Tcos\theta = mg`

`T sin\theta = ma`

so we will have

`tan\theta = (ma)/(mg)`

`\theta = tan^(-1)(a)/(g)`

so here the angle made by the string is independent of the mass

Part b)

Now from above equation if we know that angle made by the string is

`\theta = 23 degree`

so we will have

`tan23 = (a)/(g)`

`a = g tan23`

`a = 9.81(tan23)`

`a = 4.16 m/s^2`