How Fast is the Roller Coaster Car at the Top of the Hill?

In summary, the question asks for the speed of a roller coaster car at the top of a 10 m radius hill when its apparent weight is one-half its true weight. The equations A=v^2/r and F=ma are provided. The weight is not necessary in the calculation as it cancels out. The missing variable for the Force can be solved for by showing the attempted solution and identifying where the problem lies.
  • #1
hbteen
1
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Homework Statement



As a roller coaster car crosses on the top of a 10 m radius hill (the track is underneath the car), its apparent weight is one-half its true weight. What is the car's speed at the top?


Homework Equations




A=v^2/r
F=ma

The Attempt at a Solution



I tried saying the weight was .5 and solving for velocity, but I still have a missing # for the Force variable.
Where do I go from there?
 
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  • #2
Welcome to PF!

Hi hbteen! Welcome to PF! :smile:
hbteen said:
As a roller coaster car crosses on the top of a 10 m radius hill (the track is underneath the car), its apparent weight is one-half its true weight. What is the car's speed at the top?

A=v^2/r
F=ma

I tried saying the weight was .5 and solving for velocity, but I still have a missing # for the Force variable.

The weight doesn't matter … it cancels out. :wink:

Show us what you tried, and then we'll see where the problem is. :smile:
 
  • #3


It is important to note that in this situation, the car is experiencing two forces: its weight (mg) and the normal force from the track (N). The normal force is responsible for the apparent weight being one-half of the true weight. We can use this information to set up an equation:

N = 1/2mg

We also know that at the top of the hill, the normal force is equal to the centripetal force, which is given by:

N = mv^2/r

Combining these two equations, we can solve for the velocity at the top of the hill:

mv^2/r = 1/2mg
v^2 = gr/2
v = √(gr/2)

So the speed of the car at the top of the hill is equal to the square root of half the acceleration due to gravity (g) multiplied by the radius of the hill (r).
 

FAQ: How Fast is the Roller Coaster Car at the Top of the Hill?

1. How does a roller coaster car stay on the track?

Roller coaster cars are designed with specialized wheels that fit onto the track's rails. These wheels are positioned in such a way that they keep the car centered on the track and prevent it from derailing. In addition, the track itself is engineered with various dips, turns, and loops that use the forces of gravity and inertia to keep the car on the track.

2. What controls the speed of a roller coaster car?

The speed of a roller coaster car is controlled by a combination of gravity and the design of the track. At the beginning of the ride, the car is pulled up to the highest point by a chain or cable system. Once it reaches the top, gravity takes over and propels the car down the track. The design of the track, including elements such as hills and loops, determines the speed of the car as it moves along the track.

3. How are roller coaster cars designed to ensure safety?

Roller coaster cars are designed with safety as the top priority. They undergo rigorous testing and inspection before being used in a ride. The cars are designed to withstand high speeds, sudden drops, and tight turns. They also have safety features such as lap bars and seat belts to keep riders securely in their seats.

4. What materials are used to make roller coaster cars?

Roller coaster cars are typically made from steel, aluminum, or a combination of both. These materials are lightweight, yet strong and durable enough to withstand the intense forces of a roller coaster ride. In some cases, newer materials such as carbon fiber are being used to make roller coaster cars even lighter and stronger.

5. How are roller coaster cars tested before being used in a ride?

Roller coaster cars undergo extensive testing before being used in a ride. This includes both computer simulations and physical testing. The cars are put through various scenarios to ensure they can withstand the forces and speeds of the ride. They are also inspected for any potential flaws or issues before being approved for use.

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