Solving the Acceleration of a Bob Attached to a Train

[jinhuit95]

Homework Statement

A bob of mass 0.35 kg is attached by a string to the roof of a train that is accelerating rightwards and the mass is inclined at an angle of 15° to the left. Show that the acceleration of the train is 2.63 ms^-2.

The Attempt at a Solution

I don't know how to exactly start doing this because I don't know what concepts I should use here. Please help! :)

 

[Doc Al]

Use Newton's 2nd law. What forces act on the bob? Analyze horizontal and vertical components.

 

[jinhuit95]

How do you know what to use?? I was thinking of using mg sin θ in the first place.

 

[Doc Al]

Start by drawing a free body diagram of the bob showing all forces acting on it. What forces act on the bob?

 

[jinhuit95]

Weight and tension of the string!

 

[Doc Al]

Weight and tension of the string!

Right!

Now apply Newton's 2nd law. I suggest analyzing horizontal and vertical components separately.

 

[jinhuit95]

Alright I'll try! Can I ask you another question over here??

 

[Doc Al]

Can I ask you another question over here??

Ask away.

 

[jinhuit95]

http://via.me/-2ostlh4
http://via.me/-2ostlh4
Here's the question and I did part of it and I don't know how to continue!

 

[Doc Al]

You took moments about the bottom end of the ladder, which is good. What about the other conditions for equilibrium?

(It's a bit difficult to read your work from the diagram, so write it out here if you want further critique.)

 

[jinhuit95]

Other condition will be the upward forces = downward forces?? Am I correct??
My working was W*0.5L cos θ = Y*L sin θ + f* L cos θ and that frictional force cause a moment too??

 

[Doc Al]

Other condition will be the upward forces = downward forces?? Am I correct??

Yes.

My working was W*0.5L cos θ = Y*L sin θ + f* L cos θ and that frictional force cause a moment too??

Looks good.

 

[jinhuit95]

Yes.

Looks good.

so that means W= X+f?? And I just subt w into the above equation I did??

 

[Doc Al]

so that means W= X+f?? And I just subt w into the above equation I did??

Yep.

 

[azizlwl]

X=W
X=W/2 + W/2
Find value of W/2 in term of Y.

 

[Doc Al]

X=W

Don't neglect the friction force from the wall.

 

[azizlwl]

Taking as No friction on the wall,
If we take moment at the base,
(L/2)WCosθ=LYSinθ
W/2=YTanθ.

Then we can proof the equation.

 

[Doc Al]

Taking as No friction on the wall,
If we take moment at the base,
(L/2)WCosθ=LYSinθ
W/2=YTanθ.

Then we can proof the equation.

But that's not the problem being discussed here. The wall is rough.

 

[azizlwl]

Yes i make a mistake there.
With or without friction the equation still valid.

 

[Doc Al]

With or without friction the equation still valid.

How can you say that?