- #1

ShizukaSm

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## Homework Statement

What force must be applied in the car of the image in order to all blocks remain stationary in relation to the car? Supposed that there's no friction in all surfaces, pulleys and wheels.

## Homework Equations

Fr = ma

## The Attempt at a Solution

First thing: That's a doubt I have, since there is no friction, the force F applied on the cart won't actually affect the block m1 in anyway, right? I mean, if there was no m2, the block m1 would stand in the air while M rushed in a straight line, right?

Ok, so I made all the equations and free body diagrams:

For block m1:

[itex]T = m_1a[/itex]

For block m2(F_32 is the force that the car M exerts on block with mass m2, by the way):

[itex]\\T - P_2 = 0\\

F_{32} = m_2a[/itex]

And finally, for the car(Again, F_23 is the reaction to F_32):

[itex]F - F_{23}= Ma [/itex]

Substituting everything, I find:

[itex]F = \frac{m_2g(m2+M)}{m1}[/itex]

The answer, however, is:

[itex]F = \frac{m_2g(m1+m2+M)}{m1}[/itex]

Right, so, the thing is, I've learned that there are mainly two ways of working this kind of problem:

The first one is to look at the whole system, and only analyze the external forces. The downside is that I won't know the internal forces.

The second one is to look at each free body diagram and calculate the relevant forces. The downside being that it takes more time to do in this way.

That being said, both ways always give the same answers, they're just different paths.

However, in this case, I've noticed that if I consider the system as a whole, I will get the right answer (Since mtotal = m1 + m2 + M), when considering the free body diagrams though, the block 1 won't act on car M, so he doesn't get in.

Where am I wrong?

Thanks in advance!

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