Finding Acceleration of a Car with a Hanging Mass

[morrisj753]

Homework Statement

A point object of mass M hangs from the ceiling of a car from a massless string of length L. It is observed to make an angle θ from the vertical as the car accelerates uniformly from rest. Find the acceleration of the car in terms of θ, M, L, and g.

Diagram: http://www.aapt.org/physicsteam/2010/upload/2010_FmaSolutions.pdf (Number 9)

Homework Equations

F = ma

The Attempt at a Solution

They wanted the acceleration, so I started with
a = F / m
The only thing I need is to find F and substitute it back into the above equation. However, I don't know if the car is moving up an inclined plane or on a horizontal surface.
If it were a horizontal surface, the only force would be mg sin θ (mg cos θ and Fn (ceiling) would cancel each other out), so a = g sin θ, which is not correct. My thinking is obviously flawed, so any ideas would be helpful.
Thank you

 

[Dick]

Homework Statement

A point object of mass M hangs from the ceiling of a car from a massless string of length L. It is observed to make an angle θ from the vertical as the car accelerates uniformly from rest. Find the acceleration of the car in terms of θ, M, L, and g.

Diagram: http://www.aapt.org/physicsteam/2010/upload/2010_FmaSolutions.pdf (Number 9)

Homework Equations

F = ma

The Attempt at a Solution

They wanted the acceleration, so I started with
a = F / m
The only thing I need is to find F and substitute it back into the above equation. However, I don't know if the car is moving up an inclined plane or on a horizontal surface.
If it were a horizontal surface, the only force would be mg sin θ (mg cos θ and Fn (ceiling) would cancel each other out), so a = g sin θ, which is not correct. My thinking is obviously flawed, so any ideas would be helpful.
Thank you

If it were on an inclined plane they would tell you so. The forces acting on the ball are the string tension T and gravity mg acting down. Split T into horizontal and vertical components. Then the vertical component of T must be mg. Solve for T and put it into the horizontal component.

 

[morrisj753]

Thank you for the response, and yes, I did end up with the correct answer.

 

[SignaturePF]

Just a question. How come if you split mg into components you get the wrong answer?

 

[Dick]

Just a question. How come if you split mg into components you get the wrong answer?

The ball (just like the car) is accelerating horizontally and not accelerating vertically. So you want to split the forces into horizonal and vertical components. There's no need to split mg. It's already vertical.