how do i calculate the acceleration of a car with these variables?

Question

heres the question, A pendulum of mass,1kg,is suspended from the roof of a car travelling on a level road. An observer in the car notices the string makes an angle of 10 degrees with respect to the vertical. What is the car's acceleration?

I have no idea how these are even related let alone trying to solve this, so I really need a hand

Answer 1

At first you need to draw a picture. Please show the hanging pendulum so, that the string forms small angle with the vertical to the left; angle θ  = 10°.

Show 2 forces that acts on the pendulum at this position:

1.      W = mg – weight directed vertically down.

2.      T = tension of the string, directed toward the string up.

Now we can apply Newton’s second law and write

                                                            T + W = ma                                        (1)

To write the equation in component form let’s direct x-axis to the right (as car moves) and y-axis up.

Then for

x-axis:                                                          Tsinθ = ma                                (2)

y-axis:                                                          Tcosθ = mg                           (3)

Now we will divide equation (2) by equation (3), then we will have

                                                                       tan θ = a / g                               (4)

From this equation (5)

                                                                             a = g∙ sin θ                          (5)

Hope you could by yourself put data into this formula to get the numerical value for acceleration a.