# Circular Motion: What's the Source of Centripetal force in this?

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1. Sep 17, 2016

### vinci

[Moderator's Note: Thread moved from forum General Physics hence no formatting template]

I am trying to study Circular Motion for my exams and I'm kind of unsure about one question. The question asks what's keeping the truck in circular motion. It has to be gravity I know, but gravity being directed towards the center, shouldn't that just result in the truck falling? What keeps it INTACT to the track? I am giong to quote the actual question now.

"Figure 18.17 shows part of the track of a roller-coaster ride in which a truck loops the loop. When the truck is at the position shown there is no reaction force between the wheels of the truck and the track. The diameter of the loop in the track is 8.0 m.

a) Explain what provides the centripetal force to keep the truck moving in a circle.
b) Given that the acceleration due to gravity g is 9.8 m s-2, calculate the speed of the truck.

"

2. Sep 17, 2016

### andrewkirk

Why gravity?

What keeps the truck moving in a circle when it's at the 3 o'clock or 9 o'clock position? What about at the 5 and 7 o'clock positions? What other force(s) are acting on the truck - in particular, pushing it towards the centre of the circle (which is what centripetal means)?

3. Sep 17, 2016

### PeroK

It is gravity and, as you conclude, at this point (for an instant) the truck is in free fall. To see what's happening, imagine the track was only the right half of the loop, so that after the highest point, there is no track to the left. What would happen to the truck?

Hint: look at question b). Note that question b) refers to the speed of the truck at the highest point.

4. Sep 17, 2016

### CWatters

I think this is sufficiently close to homework that it should be moved to that section.

5. Sep 17, 2016

### vinci

I assume, the truck will go straight for a while because of inertia. So how exactly am I going to put this into words?
"It is gravity that keeps the truck in it's circular motion and inertia that drives it away from the circle. The net sum of these two forces is what keeps the truck in circular motion"

6. Sep 17, 2016

### PeroK

Inertia is not a force. The truck won't go straight for a while, it will fall in a parabola. Try drawing parabolas for the truck:

a) If it's still moving fast at the top of the loop.

b) If it's moving "too slowly" at the top of the loop.

We're still imagining there is no track on the left here, so the truck is falling through the air.

7. Sep 17, 2016

### CWatters

Centripetal force is the net force. What two forces sum to make it? Try drawing a free body diagram to the car.

8. Sep 17, 2016

### PeroK

The problem here is that the question deals with a special situation at the top of the loop where there is no normal force: this is an assumption in the question. There is only gravity acting on the truck at this point. The conundrum is why the truck doesn't fall off the track at this point.

9. Sep 17, 2016

### CWatters

Fair enough but I think it helps to understand the general principles first. It's useful to think of the centripetal force as the force required for an object to move in a circle and then consider what must happen to change the radius of motion (not to be confused with the radius of the track).

10. Sep 17, 2016

### hmmm27

At that point the truck is running parallel to the track. Its velocity is purely horizontal, as is the track(d(track)=0) ;there's no net force holding it there, nor one pushing it apart. It is neither rising, nor falling. Just like a tossed ball, at the apex, it's "weightless".

11. Sep 17, 2016

### hmmm27

The definitions of both centripetal and centrifugal tend to be a little vague, but yes, gravity is providing a positive centripetal force on the upside down bit, and a negative centripetal force on the rightside up bits.

12. Sep 17, 2016

### vinci

@PeroK If I imagine the two cases in both of them the horizontal motion will be unaffected by gravity (i am assuming there is no air resistance), the truck will vertically accelerate downwards at the same time until it hits the ground. In case a) where it is moving too fast the point x-intercept of the parabola will be far away from the track and in the latter case it will be closer to the tracks. I know that there is supposed to be a case where it will travel in a circle but i can't fathom how that would be the case and why it would not just get out of the orbit. We are not talking about geo-stationary satallites who are in orbit because of the curvature of earth falling under their path.

@hmmm27: So the answer to question 'a' would be gravity, Right?

13. Sep 17, 2016

### PeroK

This isn't helping.
You're over-thinking this a little. If, at the top of the loop, the truck has sufficient speed, then it will fly off in a parabola outside where the circular track would be. So, when you add the track, the truck is forced into the circular path.

If, however, the truck is moving too slowly, the parabola will lie inside the circle. In which case, when you add the track, the truck will leave the track until at some point it crashes back into it.

That's one explanantion why there is a minimum speed required at the highest point. If the truck isn't moving fast enough, then it does fall off the track.

14. Sep 17, 2016

### hmmm27

Oh, I wouldn't say that if I was getting marked on it, since gravity at no time is actually responsible for keeping it in the curve. It's not the Moon being kept from flying off by the Earth's gravity.

As far as visiualization is concerned, the (half) parabola's pretty good. Say you have a raised horizontal track that joins to a quarter circle track which plunges into the ground. If you push the cart fast enough that it flies off the end without actually touching the quarter circle, then that's a speed you want to be at to make it through the top of the loop in the diagram.

15. Sep 17, 2016

### PeroK

The more I look at this, the less I like question a).

There is only one point on the track (at the top) where gravity is centripetal. Hence, gravity alone acts only instantaneously. There is no finite period of time where gravity alone acts, so you cannot really say that gravity causes anything to move in a circle (unless it's an orbit, which is a very different scenario). You can only describe motion as being in a circle over a finite period of time. All motion is instantaneously in a single direction.

My example of the missing track proves this point. The motion is the same at the top of the track whether the track is missing on the left or not. If it's missing, the truck follows a parabola; and if the track is present, it moves in a circle. So, you cannot say what shape it's moving in at the top.

Anyway, the important point is to understand the physics. It is possible, if you get the speed of the truck just right, for there to be no normal force (instantaneously) at the top. Any faster and there is a normal force; any slower and the truck will leave the track. That's the key point here.

The expected answer to a) is gravity, but the wording of the question is perhaps dubious.

16. Sep 17, 2016

### hmmm27

I doubt the expected answer would be gravity, since gravity never actually helps keep the cart in the track.

17. Sep 17, 2016

### PeroK

Then you'd be wrong! Gravity is a centripetal force at the single point at the top of the loop. In this case, it is the only force at that point.

18. Sep 17, 2016

### hmmm27

I said I doubted it would be the expected answer. [edit: I am allowed to change my mind, right ? yes, I imagine it would be the expected answer : I misread the problem]

If you're going to define "centripetal force" as simply something that works against inertia, then a vector component of gravity applies to the entire upside-down bit. This could be demonstrated as an increasingly flimsy track that would break apart if the full "centrifugal force" wasn't compensated for.

Last edited: Sep 17, 2016
19. Sep 17, 2016

### PeroK

This is a homework thread, in which we are trying to help the OP.

If you want to ask questions about what is and is not a centripetal force, you need to start your own thread. Leave this one for the OP's questions.

20. Sep 17, 2016

### hmmm27

right, sorry, got sidetracked - given the simplicity of the 'b' problem, I figured 'a' would be just a general question and didn't read it through properly; answer edited.

Okay, forget parabolas for a minute.

The truck sticks to the track because of the normal force; in space, the normal force would only be created by the truck running into the curvature and getting squished into the track with a centripetal acceleration $a=v^2/r$. Give the slightest push to the truck and it will go 'round and 'round the track forever. But, it's not an orbit in the sense of gravitational pull, as you point out. (As an aside, don't dwell on it, the track could be elliptical, or it could be some massive 3D assembly of twisty inside curves)

On Earth, however we have gravity. It's the most common source of the "normal force", eg. between the person and the chair he or she's sitting on. If you bring the track down to Earth then gravity will affect whatever's put on it, as it does everything, including the normal force of truck on track.

In order to stick to the track, the normal force has to be > 0. The total force perpendicular to the tangent - rotational force plus gravitational component - must be positive. In terms of acceleration $a_r + g_θ > 0$ needs be achieved to keep it stuck to the track.

For example, at the midpoints of the circle halfway up/down, gravity - a purely vertical force - has no effect on the normal force - which is purely horizontal at that point - so the rotational velocity only has to be greater than 0. At the bottom of the circle (indeed any point in the bottom semicircle), gravity will always contribute to the normal force to an extent, the most at the bottommost point.

However at the top the full force of gravity is at play against the normal force, so $a_r > g$ is the only thing that will keep it on track.

(As an aside, I can't help but note that if the truck had a motor and brakes, it could stop at the midpoints, before continuing. Alternatively It could even loop around at a constant angular velocity. But it's easiest just to let it zoom up to the top, slowing down all the way, then come back down, speeding up all the way.)

Last edited: Sep 17, 2016