Advanced Forces Question, Forces Inside a Moving Car

[Victorzaroni]

Homework Statement

A mass m is suspended by a light string from the ceiling of a moving car of mass M which is accelerating in the horizontal direction. The string makes an angle θ with the vertical as shown below. The acceleration of the car is:
(A) mg/M
(B) gsinø
(C) g/tanø
(D) mg/(m+M)
(E) gtanø

Homework Equations

F=ma

The Attempt at a Solution

I have a free body diagram with g pointing downward along the dotted line and F pointing backwards connecting m and the head of g. I just don't know where to go from here.

 

[tiny-tim]

Hi Victorzaroni!

Hint: the acceleration of the mass m is the same as the acceleration of the car.

 

[emailanmol]

Identify the constraints .

For the block to be at rest permanently from the car frame, the net force on the block should be zero with respect to the car frame . (Why?)

Draw Free Body Diagram and solve for forces along two perpendicular directions.
Use pseudo force (Why?)(Hint given in above post)