Asimple 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°.

Part a)

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

Part b)

Explanation:

Part a)

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

so we will have

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

so we will have

6/12=1/2

step-by-step explanation:

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west