How Does Roller Coaster Physics Calculate Velocity?

At point A, all the energy is potential energy (PE = mgh). At point B, the potential energy is converted to kinetic energy (KE = 1/2mv^2). So at point B, the velocity can be calculated using the equation KE = 1/2mv^2. In summary, the conversation discusses a roller coaster diagram with 3 humps in the track and various heights at different points. Using the given information, the final velocity of the coaster at point B can be calculated using the equation KE = 1/2mv^2. The answer is 35.69m/s and the conversation also confirms that this is the correct answer.
  • #1
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1. A diagram of a roller coaster is given. In the diagram, there are 3 humps in the track. At the top of the first hump(point A) the height is 60m from the ground. Point B is at the bottom of point A and is 5m below the ground. (height from point A to B is -65m). From point B to point C is 64m. From point C to D is -67m. From point D to E is 71m.
The coaster is at rest at point A.
Vy = final velocity
Vx = initial velocity
g = acceleration due to gravity (-9.8m/s)
hxy = the difference in height from point x to point y



2. Vy2 = Vx2 + 2ghxy



3. The first question is to find the velocity of the coaster at point B.
Vy2 = 0 + 2(-9.8)(-65)xy
Vy2 = 1274
√Vy2 = √1274
Vy = 35.69m/s


all i really need is a confirmation of my answer. I don't know why but i think i might be wrong.
 
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  • #2
Yes that would be correct.

Also in your final equation, what you are essentially doing is equation KE and PE at the various points.
 

Related to How Does Roller Coaster Physics Calculate Velocity?

1. How does gravity impact roller coaster physics?

Gravity plays a crucial role in roller coaster physics. As the roller coaster car moves along the track, it experiences changes in gravitational potential energy. When the car reaches the top of a hill, it has high potential energy due to its position, and as it goes down the hill, this potential energy is converted into kinetic energy. The acceleration of the car is also affected by gravity, as it pulls the car towards the ground, causing it to speed up or slow down.

2. What is the role of velocity in roller coaster physics?

Velocity, or the speed and direction of the roller coaster car, also plays a significant role in its physics. As the car moves along the track, its velocity changes, which affects its acceleration and the forces acting upon it. For example, when the car goes around a loop, its velocity changes from horizontal to vertical, causing a change in direction and acceleration. The velocity also determines how intense the forces of acceleration and deceleration will be on the riders.

3. How do the forces of inertia and centripetal force impact roller coaster physics?

Inertia is the tendency of an object to resist changes in its state of motion, and centripetal force is the force that pulls an object towards the center of a circular path. In roller coaster physics, these forces work together to keep the car on the track and determine the shape and size of the loops and curves. The higher the inertia and centripetal force, the more intense the ride will be for the riders.

4. How do different types of roller coasters affect their physics?

Different types of roller coasters, such as wooden, steel, and hybrid, have varying track designs and materials, which can impact their physics. For example, steel roller coasters are often smoother and can reach higher speeds than wooden ones, which affects the forces acting upon the car and the riders. The shape and size of the track also play a role in the forces experienced by the car and the riders.

5. What factors influence the safety of a roller coaster from a physics standpoint?

Several factors can influence the safety of a roller coaster from a physics standpoint. These include the speed and acceleration of the car, the forces acting upon the riders, the structural integrity of the track, and the design of the ride. Engineers must consider all of these factors to ensure the safety of riders and prevent accidents or malfunctions.

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