Circular Motion of a roller coaster

In summary, the passengers in a roller coaster car will feel 55% heavier than their true weight when the car goes through a dip with a radius of curvature of 24m. To find the car's speed at the bottom of the dip, you can use the equation hmg=mg + mv^2/r, where h is the percentage increase in weight, m is the mass of the car, g is the acceleration due to gravity, v is the velocity, and r is the radius of curvature.
  • #1
aligass2004
236
0

Homework Statement



The passengers in a roller coaster car feels 55% heavier than their true weight as the car goes through a dip with a 24m radius of curvature. What is the car's speed at the bottom of the dip?

Homework Equations





The Attempt at a Solution



I have no clue as to how to start this problem.
 
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  • #2
Start by drawing a free-body diagram and examining the forces acting on the car. What do you know about the net force of an object traveling in a circle?
 
  • #3
The forces acting on the car are weight and the normal force. Also, the velocity is perpendicular to the force pushing inward, which is why the object remains circular.
 
  • #4
aligass2004 said:
The forces acting on the car are weight and the normal force. Also, the velocity is perpendicular to the force pushing inward, which is why the object remains circular.
Correct! So, do you know a relationship between force, velocity and radius for an object traveling in a circular path?
 
  • #5
I have no idea.
 
  • #6
use the equation hmg=mg + mv^2/r. for example my percentage was 35% and my radius was 30m. so .35(9.8)= v^2/30 and solve for v
 

FAQ: Circular Motion of a roller coaster

1. What is circular motion in the context of a roller coaster?

In the context of a roller coaster, circular motion refers to the movement of the roller coaster along a curved path, typically in a circular or helical shape. This motion is caused by the forces of gravity, inertia, and centripetal force acting on the roller coaster.

2. How does the speed of a roller coaster affect its circular motion?

The speed of a roller coaster directly affects its circular motion. As the roller coaster increases in speed, the centripetal force required to keep it moving in a circular path also increases. If the roller coaster is moving too slowly, it may not have enough centripetal force to complete the loop and may fall off the track.

3. What is the role of centripetal force in circular motion of a roller coaster?

Centripetal force is the force that keeps an object moving in a circular path. In the context of a roller coaster, centripetal force is provided by the track to keep the roller coaster moving along its curved path. This force acts perpendicular to the direction of motion and is necessary for the roller coaster to maintain its circular motion.

4. How does the shape of a roller coaster track affect its circular motion?

The shape of a roller coaster track can greatly affect its circular motion. A track with a steeper incline or tighter curves will require more centripetal force to keep the roller coaster moving in a circular path. The shape of the track also determines the speed at which the roller coaster can safely travel without losing its circular motion.

5. What are some safety measures taken to ensure the circular motion of a roller coaster?

To ensure the safety of riders and maintain the circular motion of a roller coaster, several measures are taken. These include designing the track with proper inclines and curves, regularly inspecting and maintaining the track, and implementing safety restraints and emergency brakes. Computer simulations and testing are also used to ensure the safety and stability of the circular motion of a roller coaster.

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