Maximum velocity at the top of a roller coaster?

In summary, the question asks for the maximum speed a roller-coaster car, with a mass of 509 kg and traveling on a track with a radius of 15m, can have at point B without leaving the track. Using the equation for the sum of forces in the radial direction, and setting the normal force equal to zero just before the car leaves the track, we can calculate the maximum speed to be approximately 12.1244m/s.
  • #1
pcandrepair
67
0

Homework Statement



A roller-coaster car has a mass of 509 kg when fully loaded with passengers.
-The radius of the circle is 15m. (See picture below)

What is the maximum speed the vehicle can have at point B and still remain on the track?
_________m/s


Homework Equations



Sum of forces in the radial direction = -m(v^2)/R



The Attempt at a Solution


There would be a normal force pointing up and mg pointing down
 

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  • #2
pcandrepair said:
There would be a normal force pointing up and mg pointing down
Right. And what will the normal force become just before the car leaves the track? Use that to calculate the maximum speed. (You already know the radius of the curve at point B.)
 
  • #3
So I set the normal force equal to zero just before it would leave the track and use..

normal - mg = m(v^2)/r masses would cancel.
0 + g = (v^2)/r
gr = (v^2)
sqrt(gr) = v

when i take the sqare root of 9.8*15 I'm getting 12.1244m/s which sounds reasonable.
 
  • #4
Sounds good to me.
 

Related to Maximum velocity at the top of a roller coaster?

1. What is the maximum velocity at the top of a roller coaster?

The maximum velocity at the top of a roller coaster is the fastest speed that the train reaches at the highest point of the track. This can vary depending on the design and height of the roller coaster.

2. How is the maximum velocity at the top of a roller coaster calculated?

The maximum velocity at the top of a roller coaster is calculated using the principles of physics, specifically the conservation of energy and the laws of motion. The height, mass, and velocity of the train are taken into account to determine the maximum velocity at the top of the coaster.

3. What factors can affect the maximum velocity at the top of a roller coaster?

The maximum velocity at the top of a roller coaster can be affected by several factors, such as the height and steepness of the track, the weight and speed of the train, and external forces like wind resistance. The type of propulsion system and the presence of friction also play a role in determining the maximum velocity.

4. Is the maximum velocity at the top of a roller coaster the same for all riders?

No, the maximum velocity at the top of a roller coaster can vary for different riders. Factors such as the weight and position of the rider in the train can affect the overall speed of the train, and therefore the maximum velocity at the top of the coaster.

5. Why is the maximum velocity at the top of a roller coaster important?

The maximum velocity at the top of a roller coaster is important because it contributes to the overall thrill and excitement of the ride. It also affects the forces experienced by the riders, such as g-forces, which can add to the overall intensity of the experience. Additionally, understanding and controlling the maximum velocity can help ensure the safety of the riders.

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