Pendulum measuring acceleration of car

• oreo
In summary, a pendulum is hung by roof of a train having mass 1 kg . The train then accelerates and the pendulum makes an angle with vertical. What is acceleration of train?

oreo

This was originally posted in a non-homework forum and does not use the template.
I came across this problem which says" A pendulum is hung by roof of a train having mass 1 kg . The train then accelerates and pendulum makes an angle with vertical. What is acceleration of train? " Is it equal to gsinθ?

See, you're understanding vectors, and which components mean what.

Bystander said:
See, you're understanding vectors, and which components mean what.
So was I right. I searched for it over internet which says about using tan instead of sin but it seemed unreasonable to me
Thank you.

shayan haider said:
My bad. What you found about tan is correct. The gravitational force is perpendicular to the train's acceleration. The force acting on the pendulum mass is the vector sum of the gravitational force and the train's acceleration.
Mea culpa.

Bystander said:
My bad. What you found about tan is correct. The gravitational force is perpendicular to the train's acceleration. The force acting on the pendulum mass is the vector sum of the gravitational force and the train's acceleration.
Mea culpa.
What did you mean by that. I want to learn which is correct gsintheta or gtantheta.

shayan haider said:
gtantheta.
The vector triangle to be examined has three sides: 1) the hypotenuse, which is the resultant of gravitational force on the pendulum, and the train's acceleration (pulling the mass toward rear of train); 2) the vertical leg, which is mg of the pendulum; and 3) the horizontal leg, which is atrainm. The relationship between the two legs of the triangle is "opposite" (horizontal) over "adjacent" (vertical), or tangent, since the angle of the resultant is measured from the vertical.

Bystander said:
The vector triangle to be examined has three sides: 1) the hypotenuse, which is the resultant of gravitational force on the pendulum, and the train's acceleration (pulling the mass toward rear of train); 2) the vertical leg, which is mg of the pendulum; and 3) the horizontal leg, which is atrainm. The relationship between the two legs of the triangle is "opposite" (horizontal) over "adjacent" (vertical), or tangent, since the angle of the resultant is measured from the vertical.
Oh sorry, I have got your point. You are right. Thanks for correction.

Bystander said:
The vector triangle to be examined has three sides: 1) the hypotenuse, which is the resultant of gravitational force on the pendulum, and the train's acceleration (pulling the mass toward rear of train); 2) the vertical leg, which is mg of the pendulum; and 3) the horizontal leg, which is atrainm. The relationship between the two legs of the triangle is "opposite" (horizontal) over "adjacent" (vertical), or tangent, since the angle of the resultant is measured from the vertical.
I mistook that first. g is not the resultant. It is component.

shayan haider said:
I mistook that first. g is not the resultant. It is component.
You and me both, but it's straightened out now.