# Motion in a Circle: Find Slowest Speed for Roller Coaster

• fern
In summary, The conversation was about a person struggling with a holiday homework question involving a roller coaster track in the shape of a vertical circle. They eventually figure out that the slowest speed the roller coaster can have at the top of the loop is 5.86 m/s, and that the centripetal force must equal the roller coaster's weight. There was some confusion due to an incorrect answer given in the back of the book.
fern
heh! this is my first post!
ok... I've been trying to do this for ages, i think I am just doing it the wrong way... its holiday homework so i couldn't ask my teacher
i drew a diagram but i think i did it wrong... I am just not getting the right answer!
ok here it is
part of a roller coster track is in the shape of a vertical circle of radius 300m. what is the slowest speed the roller coster can have at the top of the loop so that all the centripetal force is supplied by the roller coaster's weight?
could someone please explain how to do this!
stank you!

Allright:
Given velocity and radius of the circle you're moving on; what's the centripetal ACCELERATION you experience?

As far as I know the answer is
centripetal force=weight
mv^2 /r= mg
v=54.221 m/s

Looks good to me; the answer is wrong.

argh! thank you! heheh that answer (5,86) was in the back of the book! i hate it when they make mistakes it just confuses me!
i propbaly would have got it if the answer was right!
thank you so much!

## 1. What is motion in a circle?

Motion in a circle refers to the movement of an object along a circular path. This type of motion is characterized by a constant speed and a continuous change in direction.

## 2. How is motion in a circle related to roller coasters?

Roller coasters use motion in a circle to create thrilling and exciting rides. The circular motion of the roller coaster cars allows for a variety of drops, twists, and turns, providing an adrenaline-filled experience for riders.

## 3. What is the slowest speed a roller coaster can go?

The slowest speed a roller coaster can go depends on several factors, such as the size and shape of the track, the weight of the cars, and the force of gravity. However, typically, roller coasters maintain a minimum speed of around 5-10 miles per hour to prevent stalling or getting stuck on the track.

## 4. How is the slowest speed for a roller coaster calculated?

The slowest speed for a roller coaster is calculated using the centripetal force equation, which takes into account the mass of the roller coaster cars, the radius of the track, and the velocity of the cars. By adjusting these variables, engineers can determine the slowest safe speed for a roller coaster without compromising the experience for riders.

## 5. Can the slowest speed for a roller coaster change?

Yes, the slowest speed for a roller coaster can change depending on external factors such as weather conditions, maintenance of the track, and the weight of the riders. Roller coaster engineers continuously monitor and adjust the speed to ensure the safety and enjoyment of riders.

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