Car moving with two blocks attached to it.

In summary, the string will keep the blocks from falling by applying tension to the rope. The tension depends on the acceleration of the block.
  • #1
ShizukaSm
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Homework Statement


Car.PNG

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!
 
Last edited:
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  • #2
ShizukaSm said:

Homework Statement


View attachment 54666
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?
That's true, so the idea is to make sure that the tension in the rope just keeps m2 from falling. Then that tension will also keep m1 stationary with respect to the cart.

What tension in the rope will keep block m2 from falling? (What tension balances the vertical components of its FBD?)

What acceleration of m1 will produce this tension? (think inertial force)
 
  • #3
Right! But in fact, I did that. P2 = T means it will remain stationary (I actually wrote that as P2 - T = 0, but it's the same thing of course). I also found the acceleration correctly.

My biggest problem was, as I said, the last part when analyzing the big cart alone.
 
  • #4
The string presses the pulley: it is attached to the cart, so the cart experiences force from the tension in he string.

ehild
 
  • #5
Wow, that is... amazing, and does make sense. That is truly amazing, thanks a lot!
 
  • #6
You are welcome :)

ehild
 

FAQ: Car moving with two blocks attached to it.

1. How does the weight of the blocks affect the car's movement?

The weight of the blocks attached to the car will increase the overall mass of the car. This will require more force to accelerate the car and will also affect its top speed. The heavier the blocks, the slower the car will accelerate and the lower its top speed will be.

2. How does the placement of the blocks on the car affect its movement?

The placement of the blocks on the car can affect its center of gravity, which can impact its stability and handling. If the blocks are placed too far from the car's center, it may become more difficult to steer and control.

3. Can the car's acceleration be affected by the surface it is moving on?

Yes, the surface the car is moving on can affect its acceleration. A smoother surface with less friction will allow the car to accelerate more easily compared to a rougher surface with more friction, which will require more force to move the car forward.

4. How do the blocks affect the car's fuel efficiency?

The weight of the blocks can affect the car's fuel efficiency. The more weight the car has to move, the more fuel it will require. This is because the car's engine has to work harder to move the extra weight, using up more fuel in the process.

5. Can the car's braking distance be affected by the blocks?

Yes, the weight and placement of the blocks on the car can affect its braking distance. The heavier the car, the longer it will take to come to a complete stop. Additionally, if the blocks are placed too far from the car's center, it may cause the car to lose balance and take longer to brake.

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