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- Homework Statement
- Which of the following statements is true regarding a rider in a roller coaster cart moving with a constant speed through a loop?

- Relevant Equations
- (Choice A)

The sum of all the forces acting on the rider is zero.

(Choice B)

The rider is accelerating.

(Choice C)

Gravity is the only force doing work on the rider.

(Choice D)

There are two forces acting on the rider, but neither does any work on the rider.

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The answer is Choice B, which makes sense; I'm just trying to figure out why C is not true.

Why I think gravity *is* the only force doing work on the rider:

1) The only forces acting on the rider are gravity and the normal force. Broken down into their component vectors, we have:

-> The component of the force of gravity moving parallel to the rider's direction of motion

-> The normal force, and the perpendicular component of gravity, acting in the perpendicular direction to the rider's direction of motion.

Thus, since Work is only the F applied in the direction of motion, gravity is the only force doing work on the rider.

But my guess is that perhaps something about the direction always changing means that the normal force is doing work on the rider by some definition? But that doesn't make sense to me because normal force will always be acting perpendicular to resulting displacement vector of its applied force.

1) The only forces acting on the rider are gravity and the normal force. Broken down into their component vectors, we have:

-> The component of the force of gravity moving parallel to the rider's direction of motion

-> The normal force, and the perpendicular component of gravity, acting in the perpendicular direction to the rider's direction of motion.

Thus, since Work is only the F applied in the direction of motion, gravity is the only force doing work on the rider.

But my guess is that perhaps something about the direction always changing means that the normal force is doing work on the rider by some definition? But that doesn't make sense to me because normal force will always be acting perpendicular to resulting displacement vector of its applied force.