Object hangs from rope on a railroad car

[cassienoelle]

Homework Statement

A 7.3 kg object hangs at one end of a rope that is attached to a support on a railroad car. When the car accelerates to the right, the rope makes an angle of 7.8 degrees with the vertical, as shown in the figure below.

(attached)

What is the acceleration of the railroad car in m/s2?

Homework Equations

The Attempt at a Solution

 

[PICsmith]

If you don't know where to begin, try drawing a free body diagram in the rest frame of the mass, where the acceleration of the car is a force acting on the mass. What other force(s) are at play? Again, show what you've tried so far or tell us where you're stuck if you want more help.

 

[Matterwave]

You can think of the acceleration producing a "fictitious force" in the opposite direction: F=ma. As PICsmith suggested, draw a free body diagram with this fictitious force to determine what it is.

 

[cassienoelle]

No one is helping.
I have NO IDEA WHAT I'M DOING.
I don't understand physics.
I don't understand gravity.
I
DON'T
UNDERSTAND
ANY
OF
THIS.

 

[Doc Al]

What forces act on the object? (Hint: only two forces act, what are they?)
Draw a free body diagram.
Apply Newton's 2nd law. (Hint: Apply it to both the horizontal and vertical directions.)

 

[cassienoelle]

so gravity is in the vertical direction down.
and acceleration is in the horizontal direction straight to the right
and mass is at angle theta from the y axis?

 

[Doc Al]

so gravity is in the vertical direction down.
and acceleration is in the horizontal direction straight to the right

Correct.

and mass is at angle theta from the y axis?

The rope is at that angle, yes.

You mentioned gravity, but what other force acts on the mass?

 

[cassienoelle]

Other than gravity? Um, the acceleration. That's all I can think of. And the mass of the ball.

 

[Doc Al]

Other than gravity? Um, the acceleration. That's all I can think of. And the mass of the ball.

Acceleration is not a force. (Neither is mass, but it does allow us to calculate the force of gravity.) Hint: What's touching the ball?

 

[PICsmith]

What forces act on the object? (Hint: only two forces act, what are they?)

Well, if we're in a reference frame on the railroad car, there's three forces acting on the mass: gravity (downward), the "fictitious" force caused by the train's acceleration (to the left, not right...that's why the mass has swung to the left), and one more force that, as Doc Al said, is caused by something touching the mass.

This is a statics problem since the mass isn't moving (in the train's reference frame). Thus, the sum of all three forces is zero. That's your equation, and you want to solve for the "fictitious" force, which will give you the acceleration of the train (by dividing by the mass, of course).

 

[Doc Al]

Unless the OP has explicitly covered the use of 'fictitious' forces and non-inertial reference frames in his course--which I highly doubt--I recommend sticking to an inertial frame for this problem.