How Fast Will the Roller Coaster Car Be at the Top of the Loop?

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In summary, a 300 kg car with an initial speed of 20 m/s enters a vertical, circular loop with a diameter of 24 m. Using the equations for kinetic and gravitational energy, it can be determined that the car will not have enough energy to reach the top of the loop. A negative answer may indicate that the car will not make it to the top. Alternatively, one can determine the maximum height the car can reach by asking if it has enough initial kinetic energy to reach the top.
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Homework Statement

At one point in a roller-coaster, a single 300 kg car goes around a vertical, circular loop with a diameter of 24 m. It enters the loop at the bottom with a speed of 20 m/s. What will its speed be at the top?

Homework Equations

Kinetic Energy = 1/2mv^2
Gravitational Energy = mgh

The Attempt at a Solution

Initial Energy = Final Energy => Kinetic Energy of the Bottom = Kinetic Energy of the Top + Gravitational Energy at the Top

I set up the equation for this problem and plugged in numbers to solve this, but I have a negative answer under the square root. Am I missing something else here?

You are right, that car will not reach the top.

Or, another way, what is the highest the car can reach?

1. How does a roller coaster loop loop work?

A roller coaster loop loop works by using the train's momentum and centripetal force to keep the riders moving in a circular motion. The train enters the loop with enough speed and momentum to make it to the top, and the circular shape of the loop ensures that the riders continue moving in a loop without falling out.

2. What are the forces acting on riders during a loop loop?

The main forces acting on riders during a loop loop are centripetal force, which keeps the riders moving in a circular motion, and gravity, which pulls the riders towards the ground. In addition, there may be some lateral G-forces as the riders go through the loop, which can cause a feeling of weightlessness or heaviness.

3. How are roller coaster loops designed to be safe?

Roller coaster loops are designed with safety as the top priority. Engineers use mathematical calculations and computer simulations to ensure that the loop is structurally sound and can handle the forces exerted on it. The loop is also designed with a specific radius and shape to ensure that the train can make it through without any issues.

4. What are the different types of roller coaster loops?

There are several different types of roller coaster loops, including vertical loops, inclined loops, and twisted loops. Vertical loops are the most common, where the track goes completely upside down, while inclined loops are at an angle. Twisted loops are more complex and involve a combination of twists and turns.

5. What are some safety precautions for riding a roller coaster loop loop?

Before riding a roller coaster loop loop, you should always follow the safety instructions provided by the ride operator. This may include securing all loose items, keeping your head and body inside the train at all times, and keeping your hands and feet in the designated areas. It's also important to follow any height or weight restrictions to ensure a safe ride.

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