# Super Fun Rollercoaster Problem

• eglaud
The mass is always positive, so the force must be positive to make the left side equal the right side.In summary, the roller coaster car is going over the top of a 14-m-radius circular rise, and at the top of the hill, the passengers feel light with an apparent weight only 60% of their true weight. The normal force is always away from the surface and can only push on an object. In this example, the roller coaster is on the outside and "down" is chosen as positive. The net force is mg - N, with the right side being positive and equal to mv2/r. The acceleration is also positive at the top of the track and negative at the bottom.
eglaud

## Homework Statement

A roller coaster car is going over the top of a 14-m-radius circular rise. At the top of the hill, the passengers "feel light," with an apparent weight only 60 % of their true weight. How fast is the rollar coaster going?

My problem first is I am unsure where the normal force is going - my professor said that with centrifical motion the normal force is always inwards, but I remember when we did this problem he made it upwards. Then, he set mg - N = mv2/r. I just don't understand how he got the left side, why is it mg - N and not the other way around? Does it matter?

a=v2/r

## The Attempt at a Solution

N=1.5mg

N - mg = mv2/r

0.5(mg) * r = v2

To begin with, the normal force is always away from the surface. A surface cannot pull on an object, it can only push on it. At the top of the track there are two possibilities
(a) If the roller coaster is on the outside, the normal force is up opposite to gravity.
(b) If the roller coaster is on the inside, the normal force is down, in the same direction as gravity.

In the example that your professor showed you it seems that the roller coaster was on the outside. It also seems that he assumed that "down" is positive. In that case the normal force is "up" (negative) and the weight (down) is positive. Thus, the net force is mg - N. The right side is positive (down towards the center) and equal to mv2/r. So mg - N = mv2/r.

kuruman said:
To begin with, the normal force is always away from the surface. A surface cannot pull on an object, it can only push on it. At the top of the track there are two possibilities
(a) If the roller coaster is on the outside, the normal force is up opposite to gravity.
(b) If the roller coaster is on the inside, the normal force is down, in the same direction as gravity.

In the example that your professor showed you it seems that the roller coaster was on the outside. It also seems that he assumed that "down" is positive. In that case the normal force is "up" (negative) and the weight (down) is positive. Thus, the net force is mg - N. The right side is positive (down towards the center) and equal to mv2/r. So mg - N = mv2/r.
Okay, what you said about the N makes a lot of sense, thanks! As for the question, you're saying that the ma is positive as well, but why?

Because in this example "down" has been chosen as positive. When the roller coaster is at the top of the track, its acceleration is towards the center which is "down", therefore positive. When the roller coaster is at the bottom of the track, its acceleration is still towards the center which in this case is "up" therefore negative.

## 1. What is the Super Fun Rollercoaster Problem?

The Super Fun Rollercoaster Problem is a hypothetical scenario used in mathematics and physics to demonstrate concepts such as conservation of energy and forces on objects in motion. It involves a rollercoaster car traveling along a track with various inclines, declines, and loops.

## 2. What is the purpose of the Super Fun Rollercoaster Problem?

The purpose of the Super Fun Rollercoaster Problem is to provide a real-world example for students to apply their knowledge of physics and mathematics. It helps them understand how forces and energy work in a dynamic system and how to solve problems using equations and principles.

## 3. What are the main components of the Super Fun Rollercoaster Problem?

The main components of the Super Fun Rollercoaster Problem are the rollercoaster track, the rollercoaster car, and the forces acting on the car, such as gravity, normal force, and friction. The problem also involves calculating the potential and kinetic energy at different points along the track.

## 4. How is the Super Fun Rollercoaster Problem solved?

The Super Fun Rollercoaster Problem is typically solved using equations and principles from physics and mathematics, such as the conservation of energy and Newton's laws of motion. Students may also use graphical methods or computer simulations to analyze the problem and make predictions.

## 5. What can we learn from the Super Fun Rollercoaster Problem?

The Super Fun Rollercoaster Problem teaches us about the laws of physics and how they apply to real-world situations. It also helps us develop problem-solving skills and critical thinking abilities. Additionally, it can be used to demonstrate the importance of safety and engineering in designing amusement park rides.

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