# What is meant by "the body is on the point of ...." in mechanics?

• etotheipi
In summary, the conversation discusses the use of the phrase "on the point of" and its relation to constraint forces in mechanics. The phrase is used to describe the exact point where the constraint forces can no longer constrain the motion of a body, and it is often used to determine when a body will slip, topple, or change direction. The speaker suggests that this terminology may be due to the inflection point in the plot of the motion versus time.
etotheipi
I see this sort of wording a lot, for instance, we might say that the block is on the point of slipping or the ball is on the point of leaving the surface of the hill. My guess is that it's to do with constraint forces; that is, at the exact point where the constraint forces acting on a body can no longer constrain the motion of the body (perhaps because static friction has reached ##\mu N## or the normal contact force has reduced to zero), we say the body is on the point of doing something.

For instance, if a ball is rolling down a hill, there exists a normal contact constraint force (satisfying ##N \geqslant 0##) which adjusts its magnitude so that the ball remains on the surface - the constrained motion. But when this force reaches ##N=0##, if the velocity of the ball increases by ##dv## the normal force according to the constrained model would become negative - which evidently can't occur.

So my conclusion was that generally we write the equations of motion for the constrained motion (i.e. at rest, moving in a circle of fixed radius, moving with a platform etc.), and then substitute in the limiting case of a constraint force to solve for the conditions when the motion becomes unconstrained. Is this what is meant when we say something is on the point of e.g. slipping/toppling etc.?

I tried searching for references but the only mentions of constraint forces I could find were in the context of Lagrangian dynamics and other higher level mechanics. I don't know if the usage in that context is similar to what I've said above.

etotheipi
PeroK said:

Fair enough, thanks for your stamp of approval!

etotheipi said:
we might say that the block is on the point of slipping
etotheipi said:
So my conclusion was that generally we write the equations of motion for the constrained motion (i.e. at rest, moving in a circle of fixed radius, moving with a platform etc.), and then substitute in the limiting case of a constraint force to solve for the conditions when the motion becomes unconstrained. Is this what is meant when we say something is on the point of e.g. slipping/toppling etc.?
I also think that you have a good grasp of what the term entails. There are other similar terms that I can think of -- "On the edge", "On the brink", "On the precipice" that all can be used to indicate the point where something changes in a situation that causes a change in motion or whatever.

Maybe one reason for the terminology of "point" or "edge" etc., is that if you plot the motion of the object versus time, there is an inflection in that plot at that "point". Certainly if you plot the position as a function of time of an object resting on a floor with friction as you linearly increase the horizontal force on it, that function will have an inflection point as the threshold force is reached to break it free and start moving it horizontally...

etotheipi and Lnewqban

## 1. What is meant by "the body is on the point of ...." in mechanics?

In mechanics, the phrase "the body is on the point of..." refers to the state of an object when it is about to undergo a change in motion. This could mean that the object is about to start moving, stop moving, or change direction.

## 2. How is "the body is on the point of ...." related to Newton's first law of motion?

According to Newton's first law of motion, an object will remain at rest or in uniform motion unless acted upon by an external force. When we say "the body is on the point of...", it means that the object is in a state where it is about to be acted upon by an external force and its motion will change accordingly.

## 3. Can you give an example of "the body is on the point of ...." in real life?

One example of "the body is on the point of..." in real life is when a person is standing on a skateboard that is on a slight incline. The person and the skateboard are both at rest, but the slightest push or disturbance can cause the skateboard to start rolling down the incline, changing the person's motion.

## 4. How is "the body is on the point of ...." different from "the body is in motion"?

The phrase "the body is on the point of..." refers to the state of an object right before a change in motion, while "the body is in motion" refers to the state of an object that is already moving. In other words, "the body is on the point of..." implies a potential for change in motion, while "the body is in motion" implies an existing motion.

## 5. What factors can influence whether "the body is on the point of ...."?

The factors that can influence whether "the body is on the point of..." include the object's mass, velocity, and the presence of external forces such as friction, gravity, or applied forces. These factors can affect the object's inertia and its tendency to remain at rest or in motion until acted upon by an external force.

• Mechanics
Replies
17
Views
2K
• Mechanics
Replies
1
Views
736
• Mechanics
Replies
22
Views
2K
• Mechanics
Replies
3
Views
938
• Mechanics
Replies
10
Views
809
• Mechanics
Replies
2
Views
1K
• Mechanics
Replies
1
Views
1K
• Mechanics
Replies
2
Views
1K
• Classical Physics
Replies
10
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
1K