Calculating Forces on a Moved Body

[fisica15]

I have a body moved by a crane hook and I want to represent the forces that act on the body in the case of translation, rotation and roto translation. Can someone help me?
Thank you

[Moderator's note: moved from a technical forum.]

 

[BvU]

Hello @fisica15 ,

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We will be glad to help, but we do need a complete problem statement to guide you in solving (as opposed to writing a chapter like for a textbook). So: what is it you want to do ?

Another helpful action is to provide a sketch of the situation.

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[fisica15]

Ok, so here you can see a scheme of my problem. I need to show graphically the forces that are applied on the hook that sustains the mass M. I have three cases to work on:
A) the crane is not moving, only the rope is moving vertically to lift and to lower the weight
B) now the crane is moving on a plane on the left or on the right, now the rope is not moving vertically
C)Now the crane is moving on the horizontal direction and the rope is moving on the vertical direction, so basically is a combination of point A and B
Ps: don't consider the two weights m.
Thank you

 

[BvU]

Well, starting with case A:
Assuming the load is moving upwards with a constant velocity:
Which things exert forces on the hook ? In which direction ?

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[fisica15]

Well, starting with case A:
Assuming the load is moving upwards with a constant velocity:
Which things exert forces on the hook ? In which direction ?

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the crane moves the rope up : there's the tension on the rope and the weight of the mass M. The forces are on the axis of the rope, the weight goes down and the tension goes up. This is what i think is true

 

[Lnewqban]

Welcome!
Are you sure the problem asks for forces on the hook?
The hook can only pull, more or less, in one single direction; therefore, only one force can be acting on it.

 

[fisica15]

Welcome!
Are you sure the problem asks for forces on the hook?
The hook can only pull, more or less, in one single direction; therefore, only one force can be acting on it.

I know, but when the crane is moving horizontally, then the forces applied on the hook will have different angles i guess and i think there will be also a rotation of the hook

 

[BvU]

the crane moves the rope up : there's the tension on the rope and the weight of the mass M. The forces are on the axis of the rope, the weight goes down and the tension goes up. This is what i think is true

Something like this ?

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[fisica15]

Something like this ?

View attachment 288386
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yes, exactly

 

[jbriggs444]

only one force can be acting on it.

At least two, surely.

If one expects the hook to accelerate or to rotate or swing then the one expects the forces to sum to something different from zero and for the individual lines of action not to all pass through the center of mass of the hook.

 

[BvU]

I estimate that would become too complicated. Propose to treat the hook as massless.
Agree, @fisica15 ?

B) now the crane is moving on a plane on the left or on the right, now the rope is not moving vertically

If you experiment with a mass on a string, you can see how hard it is to move the suspension point (your hand) from one position to another without making the mass go into a swinging motion.
Can you propose a suitable FBD for a massless hook ?

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[fisica15]

I estimate that would become too complicated. Propose to treat the hook as massless.
Agree, @fisica15 ?If you experiment with a mass on a string, you can see how hard it is to move the suspension point (your hand) from one position to another without making the mass go into a swinging motion.
Can you propose a suitable FBD for a massless hook ?

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By the way, I was already considering a massless hook, the weight is given by the mass moved by the hook. Then, i prefer to consider a realistic situation for my work and in fact, in reality you can see that an object moved by a crane tends to oscillate, because the rope, the hook and the mass tends to behave as a pendulum.

 

[haruspex]

By the way, I was already considering a massless hook, the weight is given by the mass moved by the hook. Then, i prefer to consider a realistic situation for my work and in fact, in reality you can see that an object moved by a crane tends to oscillate, because the rope, the hook and the mass tends to behave as a pendulum.

Trust me, there are far more interesting aspects to discuss than the consequences of the mass of the hook. Don't try to be completely realistic straight off.

Is the mass being moved at a uniform rate or is it accelerating in the given direction ?
Is air resistance to be considered?
What about the crane rotating about a vertical axis?
And you already mentioned oscillation.

Let's start with something simple: horizontal movement at a steady speed, no air resistance, no oscillation.

 

[fisica15]

Trust me, there are far more interesting aspects to discuss than the consequences of the mass of the hook. Don't try to be completely realistic straight off.

Is the mass being moved at a uniform rate or is it accelerating in the given direction ?
Is air resistance to be considered?
What about the crane rotating about a vertical axis?
And you already mentioned oscillation.

Let's start with something simple: horizontal movement at a steady speed, no air resistance, no oscillation.

I don't understand if you're talking about the mass of the hook (that i didn't considered honestly) or if you're referring to the mass M moved by all the system.
If we start at a basic level with an horizontal movement at a constant speed and no oscillation, i would say that the weight force and the tension stay in the same conifguration. Is it ok?

 

[haruspex]

I don't understand if you're talking about the mass of the hook (that i didn't considered honestly) or if you're referring to the mass M moved by all the system.
If we start at a basic level with an horizontal movement at a constant speed and no oscillation, i would say that the weight force and the tension stay in the same conifguration. Is it ok?

Ok, so what next? Horizontal acceleration? Air resistance? Rotation? Oscillation? Movement in more than one dimension?

 

[fisica15]

Ok, so what next? Horizontal acceleration? Air resistance? Rotation? Oscillation? Movement in more than one dimension?

let's avoid to consider the air resistance and let's consider the case in which we have oscillation and horizontal acceleration

 

[BvU]

As in #2: a specific case is more suitable for treatment here in PF. So with #16 we have a good candidate.

Basically we are dealing with a pendulum with a movable suspension point. Already anything but trivial. As a further complication there is the possible variation of length.

A good tool set in this context is provided in Lagrangian mechanics, with which I expect the OP is not familiar (right?).

And a google search for e.g. swing suppression in cranes reveals an extensive research area.

Now what ? ...

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[haruspex]

let's avoid to consider the air resistance and let's consider the case in which we have oscillation and horizontal acceleration

Ok.
Can you see an easy way to deal with (small) oscillation and constant acceleration?

 

[fisica15]

Ok.
Can you see an easy way to deal with (small) oscillation and constant acceleration?

like an helicoidal movement?

 

[haruspex]

like an helicoidal movement?

No, I meant the trolley accelerating horizontally, uniformly, steady state.
Or maybe a more practical model would be starting with M at rest and the trolley then moving at constant speed?

 

[fisica15]

No, I meant the trolley accelerating horizontally, uniformly, steady state.
Or maybe a more practical model would be starting with M at rest and the trolley then moving at constant speed?

ok, let's try with the second one

 

[jbriggs444]

ok, let's try with the second one

So we have a trolley moving at a constant speed (let's say rightward) and we have a mass that is initially hanging motionless beneath.

My first move when analyzing this problem would be to change to a frame of reference in which the trolley is fixed and motionless and the mass starts directly beneath it but moving leftward. Does this reduce the problem to something simpler?

 

[fisica15]

So we have a trolley moving at a constant speed (let's say rightward) and we have a mass that is initially hanging motionless beneath.

My first move when analyzing this problem would be to change to a frame of reference in which the trolley is fixed and motionless and the mass starts directly beneath it but moving leftward. Does this reduce the problem to something simpler?

As a first analysis it can be ok, but then I need to analyze graphically something more complex

 

[jbriggs444]

As a first analysis it can be ok, but then I need to analyze graphically something more complex

This goes counter to everything that I hold dear. When analyzing or understanding a problem, one wants to simplify, not complicate.

 

[fisica15]

This goes counter to everything that I hold dear. When analyzing or understanding a problem, one wants to simplify, not complicate.

ok, so how would you do that problem? let me know...

 

[jbriggs444]

ok, so how would you do that problem? let me know...

What problem? I thought that you had agreed that we were talking about the "second problem" in #20:

Or maybe a more practical model would be starting with M at rest and the trolley then moving at constant speed?

Which you seemingly agreed to in #21

ok, let's try with the second one

I told you how I would approach that problem. You objected and now want to know how I would approach that problem.

So I guess I am confused.

It is often difficult to keep things straight when faced with references like "the second one" or "my other posting" (this is a general frustration, not something specific to you) without adding enough context or an actual quote to clearly identify the reference. It is painful having to scroll up and down through a thread to try to gather enough context to make a meaningful contribution.

 

[Lnewqban]

I know, but when the crane is moving horizontally, then the forces applied on the hook will have different angles i guess and i think there will be also a rotation of the hook

It seems that the problem is not asking you to calculate anything, only to show forces and directions in which they act.

If that is the case, those movements could be accelerated (always happens when starting movement from repose, or when stopping movement) or of constant speed (after the first seconds, cranes pull or move at a constant velocity, just as their engines do).

If acceleration-horizontal translation is present, the wire-rope and the hook will show some angle, due to inertia of the lifted load.
If acceleration-vertical translation is present, the wire-rope and the hook will show increased or decreased tension (respect to the natural weight of the load), due to inertia of the lifted load.

None of those things should happen when acceleration is not present.
In order to have acceleration, you need a mass (which you have) and a resultant applied force on that mass.

 

[fisica15]

It seems that the problem is not asking you to calculate anything, only to show forces and directions in which they act.

If that is the case, those movements could be accelerated (always happens when starting movement from repose, or when stopping movement) or of constant speed (after the first seconds, cranes pull or move at a constant velocity, just as their engines do).

If acceleration-horizontal translation is present, the wire-rope and the hook will show some angle, due to inertia of the lifted load.
If acceleration-vertical translation is present, the wire-rope and the hook will show increased or decreased tension (respect to the natural weight of the load), due to inertia of the lifted load.

None of those things should happen when acceleration is not present.
In order to have acceleration, you need a mass (which you have) and a resultant applied force on that mass.

That's what I need! But I have some doubt on how oscillation will affect those forces (Ps: i applied the forces on the hook, because this is the point where I need to have the resultant)

 

[jbriggs444]

That's what I need! But I have some doubt on how oscillation will affect those forces (Ps: i applied the forces on the hook, because this is the point where I need to have the resultant)

But if the hook is massless then the resultant on the hook is necessarily zero. You need the resultant on something with non-zero mass.

For instance, the mass has non-zero mass.

 

[fisica15]

But if the hook is massless then the resultant on the hook is necessarily zero. You need the resultant on something with non-zero mass.

For instance, the mass has non-zero mass.

You're right, let's consider it on the mass