Roller Coaster Physics: Force & Max Speed

In summary, a roller coaster with a mass of 510kg and a speed of 19.6 m/s at point A has a force exerted by the track of 19592.16 N. To find the maximum speed at point B, we need to consider the net acceleration, which is the sum of gravitational acceleration and the acceleration due to the curve. The equation used is EF= m(v^2 / r), where v is the velocity and r is the radius of the curve. B must be on a curve that is convex down, and the maximum speed can be found by setting the two accelerations (g and v^2/r) equal to each other.
  • #1
tnhoots
36
0

Homework Statement


A roller coaster has a mass of 510kg when fully loaded with passengers. The radius at point A is 10.0 m and the radius at point B is 15.0 m.

-If the vehicle has a speed of 19.6 m/s at point A, what is the force exerted by the track on the car at this point? (N)

-What is the maximum speed the vehicle can have at B and still remain on the track? (m/s)



Homework Equations



EF=m (v^2 / r)

The Attempt at a Solution



*For the first problem I thought you would use the equation EF=m (v^2 / r). Which would be EF=510 (19.6^2 / 10.0). Which equals 510*(384.16/10.0). Equals 19592.16. However, this is wrong! Isn't that the right equation?

*For the second problem, I'm not sure where to start. But I'm assuming that I will need the correct force value before I can begin.

Any suggestion as to where I'm going wrong?
 
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  • #2
It all depends on the location of points A and B, perhaps if you could post a diagram or describe the position of the two points we could help you further.
 
  • #3
assuming a is on a curve that is convex up, (try it the other way and you'll find its off the track i think), you have two a accelerations to account for, g and the v^2/r which is 19.6^2/10=38.4. Compute the net a, then you have the force pushing on the track.

b must be convex down (or upside down, but then it would be a minimal speed): v^2/15=g as the two accelerations are opposing.
 

FAQ: Roller Coaster Physics: Force & Max Speed

1. How does gravity affect the speed of a roller coaster?

Gravity plays a major role in the speed of a roller coaster. As the coaster goes up a hill, gravity pulls it down, increasing its speed. On the way down, gravity also pulls the coaster down, increasing its speed even more. However, on level ground or during turns, the force of gravity is not as strong and the coaster's speed decreases.

2. What is the maximum speed that a roller coaster can reach?

The maximum speed of a roller coaster depends on various factors such as the height and steepness of the hills, the weight of the coaster and its passengers, and the amount of friction between the track and the wheels. Generally, modern roller coasters can reach speeds of up to 120 mph, with some even reaching speeds of over 150 mph.

3. How do forces such as acceleration and deceleration affect the riders on a roller coaster?

The forces of acceleration and deceleration are what make roller coasters thrilling. Acceleration, or the increase in speed, pushes riders back into their seats and can cause a feeling of weightlessness. Deceleration, or the decrease in speed, can cause riders to feel a strong pulling sensation and can increase the feeling of weight in their bodies.

4. How do roller coasters use potential and kinetic energy?

Roller coasters use potential energy, which is the energy an object possesses due to its position, when they are at the top of a hill. As the coaster goes down the hill, potential energy is converted into kinetic energy, which is the energy an object possesses due to its motion. This is why roller coasters are able to maintain their speed throughout the ride.

5. How do engineers design roller coasters to ensure the safety of riders?

Engineers use a variety of design elements to ensure the safety of riders on roller coasters. These include creating smooth and gradual curves, designing restraints that keep riders securely in their seats, and implementing various safety features such as brakes and sensors. Roller coasters also undergo rigorous testing and inspections before they are opened to the public.

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