Problem involving static equilibrium

[issacnewton]

Hi

I have posted the picture of the problem. I have already done the problem but I have some
questions. Here the trailer is accelerating due to the applied force P. I used an inertial frame of
reference at some distance to the left of the car.And then did the torque calculations with respect to the stationary frame. But the author's (Serway,Jewett) solution takes center of mass (CM) as the origin of the coordinate system to calculate the net torque.

Now my question is about the choice of coordinate system. Physics laws are valid in an inertial frames of references. Since the trailer is accelerating, how can we fix the coordinate system to the CM of the trailer for the purpose of calculations. In such case, we will need to come up with some pseudo forces.

Any inputs ?

thanks

 

[gneill]

Even if the trailer is accelerating, can one not assume that the pulling force P will be such that it must remain level? (otherwise it'll be a short and messy ride...)

I suppose you could make a new g, call it g', that is the vector sum of the gravitational and linear accelerations. Then your problem becomes purely static.

I would think that using the wheel as a center of rotation for the trailer would make more sense, since that's where it'll pivot. The center of mass, being away from the pivot point, will generate a torque.

 

[issacnewton]

I suppose you could make a new g, call it g', that is the vector sum of the gravitational and linear accelerations. Then your problem becomes purely static.

So do we have to come up with fictitious forces if the coordinate system is fixed to the trailer ?

 

[gneill]

So do we have to come up with fictitious forces if the coordinate system is fixed to the trailer ?

Nope. Not once you've 'transitioned' to the new g! What you see is what you get.

This is based opon the Equivalence Principle, which implies that a real acceleration is indistinguishable from a gravitational acceleration.

 

[hotvette]

You can use any orgin you want. In static equilibrium problems it is always easier to pick a point where there is an applied force (so there are fewer equations) and where the level arms are easy to calculate. I looked at the picture before reading your post and I immediately picked the CM as a convenient origin.

 

[issacnewton]

This is based opon the Equivalence Principle, which implies that a real acceleration is indistinguishable from a gravitational acceleration.

Hi I am thinking from introductory physics perspective. They don't teach equivalence principle yet, but they emphasis that Newton's laws are valid in inertial frames. So when we fix
the frame in the accelerating trailer, we are no longer in an inertial frame and to use equations of static equilibrium we need to have inertial frame since we are basically going to use Newton's
laws.

 

[PhanthomJay]

Hi I am thinking from introductory physics perspective. They don't teach equivalence principle yet, but they emphasis that Newton's laws are valid in inertial frames. So when we fix
the frame in the accelerating trailer, we are no longer in an inertial frame and to use equations of static equilibrium we need to have inertial frame since we are basically going to use Newton's
laws.

Although I am not a big fan of pseudo (ficticious) forces (especially centrifugal force!), they nevertheless seem to work well in problems of these types. Since Newton 2 tells us that F_net = ma, then it follows that that F_net -ma = 0, where 'ma' is the pseudo force placed at the center of mass in the direction opposite the acceleration (pointing left in this example). (This is a special case of D'Alembert's principle). Then you use Newton's 1st laws of (dynamic) equilibrium (Fx_net =0, Fy_net =0, and Mz_net about any point =0) to solve the problem. Be sure in your free body diagram to label the pseudo force as such; it is a 'free body diagram with pseudo forces', not a 'free body diagram'. In general, though, try to avoid pseudo forces like the plague.

 

[issacnewton]

Hi Phanthom,

Pseudo forces can be confusing . I know that equivalence principle makes gravity into a pseudo force, and since general theory of gravity (GTR) is more accurate theory of the gravity, it means gravity indeed is a fictitious force. But in basic physics course it can be confusing. May be I am wrong. It is possible that the introductory physics can be taught with the understanding of the equivalence principle. That will be an interesting approach Do you know any such book ?

 

[PhanthomJay]

Hi Phanthom,

Pseudo forces can be confusing . I know that equivalence principle makes gravity into a pseudo force, and since general theory of gravity (GTR) is more accurate theory of the gravity, it means gravity indeed is a fictitious force. But in basic physics course it can be confusing. May be I am wrong. It is possible that the introductory physics can be taught with the understanding of the equivalence principle. That will be an interesting approach Do you know any such book ?

I don't, but personally, i think it would be a bad idea...in fact, a very bad idea. But then again, I'm old school.

 

[issacnewton]

Phanthom, why is it a bad idea ? I want to know. For pedagogical reasons or other reasons ?

 

[PhanthomJay]

It's a bad idea from my perspective, because it borders on general relativity concepts, like Einstein's man in the box in a zero g environment being pulled up by a rope from afar. While it is very interesting reading, it doesn't belong in an intro physics class, where students are struggling with F = ma and W = mg. Introducing this equivalence principle is bound to confuse the student even more, just like pseudo forces...this topic belongs in an advanced physics course, or GR course, not an intro one...that's my thought anyway, others may think otherwise.