Centripetal force and Roller coasters

[princesslinda]

This question is in regards to TBR section 3 practice passage 2 question #13.

The questions is: which of the following pictures best represents the direction of the net force F acting on the cart when it is half way up the loop (at the 3 o clock position)?

I am confused because for this question I chose the answer with the Fnet pointing toward the center of the loop because I thought the net force for an object moving in a circle always points toward the center of the circle? However, the answer is the sum of the gravitational force and normal force which do not have a Fnet that points towards the center.

Can anyone tell me the reasoning behind why the Fnet would not point towards the center (as would be the case for uniform circular motion)?

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[Morsetlis]

Centripetal force points toward the center of the circle and is perpendicular to the direction of the velocity, which is itself in a tangent line to the path of the object/track. The actual movement of the object is on a circle, and you should notice that while Fc = mv^2 / r, the Fc is NOT in the same direction as the velocity of the object. The Fc is created, of course, by the actual normal force of the track. This is due to momentum: a stationary object with 0 acceleration would have 0 Fc, but an object moving against the track would elicit an opposite reaction that is the Fc.

At all times, gravity is also acting on the moving object, pulling it earthward.

Therefore, Fnet is a sum of Fc and Fg.

When the cart is halfway UP the loop, the direction for Fc points toward the center. Fg points always downward toward the earth. The Fnet is diagonally downward and toward the center.

 

[Code Blah]

Sum of forces is equal to centripetal force.

 

[Morsetlis]

Sum of forces is equal to centripetal force.

No, the centripetal force is always perpendicular to the velocity. The sum of forces is simply Fnet...

 

[superman3]

right, but the centripetal force is ALWAYS equivalent to Fnet. Recall, that the centripetal force is just the name given to the net force when an object is undergoing circular motion. (Morsetlis, you and thelittleone are saying the same thing ).

 

[Morsetlis]

It's been 6 years

 

[princesslinda]

so the centripetal force (which is the fnet) would be pointing diagonally downward?

 

[superman3]

I would have to see the picture of the loop itself, but if the loop on which the cart is traveling is not circular, or if the cart doesn't travel on the circular path uniformly (meaning that the speed is constant), then the net force would not necessarily point to the center of the circle. In that case, you would have to sum the forces contributing to the net force (i.e. gravity, normal force, as shown in the images posted by morsetlis). As for why this sum, could cause the centripetal force to point in a different direction than uniform circular motion...I think TBRteach is much more qualified to answer....

 

[Pisiform]

Essentially, the F(net) here is the resultant of both Gravitational and Centripetal force because the circular motion is performed above ground level i.e. height is not the same during the entire circular motion. Therefore, it becomes necessary to take both forces into account. Simple as that.