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

Answer:

Part a)

$\theta = tan^{-1}\frac{a}{g}$

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

Part b)

$a = 4.16 m/s^2$

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

$tan\theta = \frac{ma}{mg}$

$\theta = tan^{-1}\frac{a}{g}$

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

$tan23 = \frac{a}{g}$

$a = g tan23$

$a = 9.81(tan23)$

$a = 4.16 m/s^2$

Answer 2

Answer:

(a) g tan u

(b) 4.16 m/s^2

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