Solving for Acceleration in a Moving Railroad Car: Newton's Law Explained

[stanton]

Homework Statement

A 3kg object hangs at one end of a rope that is attached to a the ceiling of a railroad car. When the car accelerates to the right, the rope makes an angle of 4 degrees with the vertical. Find the acceleration of the car.
the answer is 0.69m/s^2

Homework Equations

sigma F=ma, tension*cos(theta) = mg, Fnet - ma = 0
yup. looks good to me. but I don't what values to plug in.

The Attempt at a Solution

First I draw free body diagram. gravity acts on the string. And I thought I could make some equation like Fsin(delta) like sort of thing by drawing triangle with 4 degree and...oh, I got all messed up.
I tried to use an equation :tension*cos(theta) = mg
plug value: tension*cos(4)=3.0x9.81 I think I can figure out what the tension is. However,
I do not know how to get the acceleration.
will you please help me?
I would be very appreciated if you give me specific procedure how the answer came out by giving information about what equation was used and so forth. Thanks!

 

[Donaldos]

The first equation you found is correct:

T \cos \theta =mg

Using Newton's second law you should also be able to show that:

ma=T sin \theta

Combine the two equations to find a.

 

[stanton]

My, I didn't know this can be solved so easily. I remember my teacher said about it, but I lost my note. When I followed your advice and used the equation i am given, I got my result 0.685! Thank you so much. Have a nice day =)