# Solving a Circular Motion Problem - Expert Tips and Techniques

• bloodlust_X
In summary, the problem involves occupants experiencing a normal force equivalent to 1/4-th of their weight while riding a rollercoaster. The question asks for the radius of the arc that the occupant's mass center is following, not the radius of the loop as a track. The mass of the rollercoaster is not relevant to the problem. The equation used by the student suggests that the centripetal force equals 1/4 of the gravitational force, but more information is needed to determine if that is correct.
bloodlust_X
Homework Statement
During the Physics Field Trip to Six Flags, Skyler and Jayson experienced a looping roller coaster ride for the first time. Their 656-kg roller coaster car was moving at 15.8 m/s at the top of the loop where occupants experienced a normal force equivalent to 1/4-th their weight. Determine the radius of curvature of the loop.
Relevant Equations
So I tried using F = mv^2/r, and f =mg to cancel mass but it didn't work, also its confusing which forces are supposed to be used?
Fnet would otherwise be 4281N, after subtracting 1/4 of rollercoaster's weight?

Please give us your actual attempt including the equations you wrote down. Show us what you did, don’t just describe it in words.

bloodlust_X said:
occupants experienced a normal force equivalent to 1/4-th their weight.

after subtracting 1/4 of rollercoaster's weight
It's the occupants that you have the normal force info on. Have you drawn a Free Body Diagram for one of those? What forces does it show?

Btw, you can't actually find the radius of the loop as a track, only the radius of arc the occupant's mass centre is following.

Orodruin said:
Please give us your actual attempt including the equations you wrote down. Show us what you did, don’t just describe it in words.

haruspex said:
It's the occupants that you have the normal force info on. Have you drawn a Free Body Diagram for one of those? What forces does it show?

Btw, you can't actually find the radius of the loop as a track, only the radius of arc the occupant's mass centre is following.
so nothing to do with the mass of the rollercoaster in the problem?

That doesn’t really tell us what you did. Please type it out with your arguments in between the equations. (See the homework guidelines)

As @Orodruin notes, posting that working doesn't tell us what principles you are using. But reverse engineering your first equation, it says centripetal force = gravitational force/4. Is that what the question says?

## 1. How do I determine the centripetal force in a circular motion problem?

The centripetal force in a circular motion problem can be determined by using the formula Fc = mv^2/r, where Fc is the centripetal force, m is the mass of the object, v is the velocity, and r is the radius of the circular path.

## 2. What is the difference between centripetal acceleration and tangential acceleration?

Centripetal acceleration is the acceleration towards the center of the circular path, while tangential acceleration is the acceleration along the tangent of the circular path. Centripetal acceleration is always present in circular motion, while tangential acceleration is only present if there is a change in speed.

## 3. How do I find the period of a circular motion problem?

The period of a circular motion problem can be found by using the formula T = 2πr/v, where T is the period, r is the radius, and v is the velocity. This formula represents the time it takes for an object to complete one full revolution around the circular path.

## 4. What is the role of friction in circular motion problems?

Friction can play a role in circular motion problems by providing the centripetal force needed to keep an object moving in a circular path. In situations where there is no other force acting as the centripetal force, friction can act as the necessary force to maintain circular motion.

## 5. How do I approach a circular motion problem if the object is moving at a constant speed?

If the object is moving at a constant speed in a circular path, the centripetal force will be equal to the tangential force. This means that the net force acting on the object is zero, and the object will continue to move in a circular path at a constant speed. In this case, you can use the formula Fc = mv^2/r to solve for any unknown variables.

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