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

[hmmm27]

So, at the end of the day, all the help we can give the OP is

When answering 'b', be sure to specify the domain, ie: "at the apex" or "within the circle".

 

[vinci]

I think this all raises more questions than there already were. I am going to go with 'gravity' while answering this and hope they just don't bring this question in the exam.(Too many confusions, specifically because of this part 'When the truck is at the position shown there is no reaction force between the wheels of the truck and the track.')

 

[andrewkirk]

(Too many confusions, specifically because of this part 'When the truck is at the position shown there is no reaction force between the wheels of the truck and the track.'

There's actually no problem with that statement. It is a clear, meaningful, scientific statement, because it talks about the forces that two bodies exert on one another. Further, it is correct.

The problem is question (a), which is unclear. A good exam strategy when faced with unclear questions is to just write down your understanding of the situation. For example here you could write something like:

Excluding friction and air resistance, the net force on the truck can be decomposed into components normal and parallel to the track.

The parallel component varies over time according to this formula <write formula> and causes the speed of the truck to vary. That component is equal to the component of the gravitational force on the truck that is parallel to the track. It is zero when the truck is at the point shown.

The normal component is always equal to <insert formula> and is a centripetal force as a result of which the truck moves in a circle. It is the sum of the normal force exerted by the track and the component of the gravitational force on the truck that is normal to the track. The former varies over time and is equal to <insert formula>. It is zero at the point shown, so the magnitude of the gravitational force is equal to that of the centripetal force.​

It would be hard for them to mark you down with an answer like that.

 

[hmmm27]

Too many confusions, specifically because of this part 'When the truck is at the position shown there is no reaction force between the wheels of the truck and the track.'

I don't get the confusion. It would be redundant to add "and only at that position" since, if at any other point there is "no reaction force" (due to the interaction with gravity), then the truck never reaches the apex.

At the apex the truck's motion is parallel to the track, at a distance of zero. Gravity's pull has canceled rotation's push. 'b' solves for the velocity necessary to achieve that.

Do feel free to worry about if it's actually "on" or "off" the track, though. Is the glass half empty or half full ? Is zero a positive or negative number ? Yes, we have no bananas.

Everybody else is annoyed at 'a', to which I propose...

Gravity provides a pseudocentripetal force to the truck at the apex. While the vector is equal to that of the track and the force is perpendicular to velocity, the motion due to gravity is elliptical at that velocity, and is not contributing to circular motion.​

Curious what your prof/teach says about it.