What is the Velocity at the Bottom of a Roller Coaster with Given Parameters?

In summary, the conversation discusses finding the velocity at the bottom of a roller coaster with a radius of 19.6 and a velocity of 14 m/s at the top. The equation Mv^2/r=mg is used to determine the velocity, but the person is unsure of how to solve it. They consider using a force body diagram and realize that potential and kinetic energy may be involved in finding the solution.
  • #1
nohkie
2
0

Homework Statement


A roller coaster with radius of 19.6 and at the top of the roller coaster the veloctiy is 14 m/s and the apparent weight is 0. Calculate the veloctiy at the bottom of the roller coast?

Homework Equations





The Attempt at a Solution


I can see that Mv^2/r=mg at the top but i don't get how to solve for the veloctiy at the bottom of the equation of mv^2/r = Fn-mg. Am I looking in the right direction? I've done the force body diagram but the only way i can see to get out the velocity is with mass, am I missing an equation?
 
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  • #2
Think about potential and kinetic energy.
 

Related to What is the Velocity at the Bottom of a Roller Coaster with Given Parameters?

1. What is vertical centripetal motion?

Vertical centripetal motion is a type of circular motion in which the object moves in a circular path while being pulled towards the center of the circle by a centripetal force.

2. What causes vertical centripetal motion?

Vertical centripetal motion is caused by a combination of a centripetal force and an initial velocity in the vertical direction. The centripetal force is responsible for pulling the object towards the center of the circle, while the initial velocity provides the object with the necessary speed to move in a circular path.

3. How is vertical centripetal motion different from horizontal centripetal motion?

The main difference between vertical and horizontal centripetal motion is the direction in which the object is moving. In vertical centripetal motion, the object moves in a circular path in the vertical direction, while in horizontal centripetal motion, the object moves in a circular path in the horizontal direction. Additionally, the forces acting on the object may differ depending on the direction of motion.

4. What is the relationship between the radius of the circle and the speed of an object in vertical centripetal motion?

The radius of the circle and the speed of an object in vertical centripetal motion are inversely proportional. This means that as the radius of the circle increases, the speed of the object decreases, and vice versa. This relationship is described by the equation v = √(gr), where v is the speed, g is the acceleration due to gravity, and r is the radius of the circle.

5. How does vertical centripetal motion relate to everyday life?

Vertical centripetal motion can be seen in many everyday activities, such as riding a roller coaster, swinging on a swing, or driving around a curved road. It is also important in understanding the motion of objects in space, such as planets orbiting around the sun.

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