Finding the Optimal Speed for a Coaster Loop: Solving for Centripital Forces

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In summary, the conversation discusses determining the speed required for a coaster to cause a normal force of 2mg at the top of a clothoid loop with a radius of 12 meters. The solution involved taking into account the direction of the coaster's acceleration to cancel out a negative value and arrive at the correct answer of 19m/s.
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mike_302
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Homework Statement


1. a) Determine the speed required by a coaster that would cause a rider to experience a normal force of 2mg at the top of a clothoid loop where the radius is 12meters.


Homework Equations





The Attempt at a Solution



http://i160.photobucket.com/albums/t161/mike_302/physicsq.jpg

That is my attempt at aa solution. Now, the only problem is that I get a square root negative... Obviously imaginary. Can't do it. But if I made the number positive, I get the right value of 19m/s for speed.

Somewhere/somehow, I need to cancel out the negative in there. Can someone explain how?

Thanks!
 
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  • #2
Hint: In which direction is the coaster's acceleration? Is that positive or negative?
 
  • #3
oh! okay. so acceleration is down. GOT IT! WOW! HUGE thanks!
 

FAQ: Finding the Optimal Speed for a Coaster Loop: Solving for Centripital Forces

1. What is a centripetal force?

A centripetal force is a force that acts towards the center of a circular motion, keeping an object moving along a curved path.

2. What are some examples of centripetal forces?

Some examples of centripetal forces include gravitational force that keeps planets in orbit around the sun, tension force in a string that keeps a ball moving in a circular motion, and friction force between tires and the road that keeps a car turning on a curved path.

3. How is centripetal force different from centrifugal force?

While centripetal force acts towards the center of a circular motion, centrifugal force is a perceived outward force that appears to push an object away from the center. However, centrifugal force is not a real force and is simply a result of inertia.

4. How is centripetal force calculated?

The formula for calculating centripetal force is Fc = mv^2/r, where Fc is the centripetal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circular path.

5. Why is understanding centripetal force important in science?

Understanding centripetal force is important in science because it helps explain many everyday phenomena, such as the movement of planets, the behavior of amusement park rides, and the formation of hurricanes. It is also essential in fields such as engineering, as it is necessary for designing and building structures and machines that can withstand centripetal forces.

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