Unit Summary:
How DO Roller Coasters Work?
While roller coasters are cruising down the tracks, it is important to realize that the roller coaster has no engine! The car is pulled to the top of the first hill at the beginning of the ride, but after that the coaster must complete the ride on its own. But how is that possible??It's possible!
It's the conversion of potential energy to kinetic energy that drives the roller coaster and the kinetic energy needed to move the roller coaster is built up once the roller coaster descends the first hill.
In this unit, we'll learn about Newton's laws of motion to understand the concepts of acceleration, speed, friction, momentum and gravity and their role in the working of roller coasters. we'll learn that energy can be converted from one form to another and energy conversion is what drives a roller coaster.
While roller coasters are cruising down the tracks, it is important to realize that the roller coaster has no engine! The car is pulled to the top of the first hill at the beginning of the ride, but after that the coaster must complete the ride on its own. But how is that possible??It's possible!
It's the conversion of potential energy to kinetic energy that drives the roller coaster and the kinetic energy needed to move the roller coaster is built up once the roller coaster descends the first hill.
In this unit, we'll learn about Newton's laws of motion to understand the concepts of acceleration, speed, friction, momentum and gravity and their role in the working of roller coasters. we'll learn that energy can be converted from one form to another and energy conversion is what drives a roller coaster.
Subject Area: Physics
Newton's Laws
The Laws of Energy and Momentum
The Laws of Energy and Momentum
Grade Level:
Grades 11-12
Targeted Content Standards:
Motion and Forces
1. Newton’s laws predict the motion of most objects. As a basis for understanding this concept:
a. Students know how to solve problems that involve constant speed and average speed.
b. Students know that when forces are balanced, no acceleration occurs; thus an object continues to move at a constant speed or stays at rest (Newton’s first law).
c. Students know how to apply the law F=ma to solve one-dimensional motion problems that involve constant forces (Newton’s second law).
d. Students know that when one object exerts a force on a second object, the second object always exerts a force of equal magnitude and in the opposite direction (Newton’s third law).
e. Students know the relationship between the universal law of gravitation and the effect of gravity on an object at the surface of Earth.
f. Students know applying a force to an object perpendicular to the direction of its motion causes the object to change direction but not speed (e.g., Earth’s gravitational force causes a satellite in a circular orbit to change direction but not speed).
g. Students know circular motion requires the application of a constant force directed toward the center of the circle.
h.* Students know Newton’s laws are not exact but provide very good approximations unless an object is moving close to the speed of light or is small enough that quantum effects are important.
Conservation of Energy and Momentum
2. The laws of conservation of energy and momentum provide a way to predict and describe the movement of objects. As a basis for understanding this concept:
a. Students know how to calculate kinetic energy by using the formula E= (1/2)mv2.
b. Students know how to calculate changes in gravitational potential energy near Earth by using the formula (change in potential energy) =mgh (h is the change in the elevation).
c. Students know how to solve problems involving conservation of energy in simple systems, such as falling objects.
d. Students know how to calculate momentum as the product mv.
e. Students know momentum is a separately conserved quantity different from energy.
f. Students know an unbalanced force on an object produces a change in its momentum.
g. Students know how to solve problems involving elastic and inelastic collisions in one dimension by using the principles of conservation of momentum and energy.
h.* Students know how to solve problems involving conservation of energy in simple systems with various sources of potential energy, such as capacitors and springs.
1. Newton’s laws predict the motion of most objects. As a basis for understanding this concept:
a. Students know how to solve problems that involve constant speed and average speed.
b. Students know that when forces are balanced, no acceleration occurs; thus an object continues to move at a constant speed or stays at rest (Newton’s first law).
c. Students know how to apply the law F=ma to solve one-dimensional motion problems that involve constant forces (Newton’s second law).
d. Students know that when one object exerts a force on a second object, the second object always exerts a force of equal magnitude and in the opposite direction (Newton’s third law).
e. Students know the relationship between the universal law of gravitation and the effect of gravity on an object at the surface of Earth.
f. Students know applying a force to an object perpendicular to the direction of its motion causes the object to change direction but not speed (e.g., Earth’s gravitational force causes a satellite in a circular orbit to change direction but not speed).
g. Students know circular motion requires the application of a constant force directed toward the center of the circle.
h.* Students know Newton’s laws are not exact but provide very good approximations unless an object is moving close to the speed of light or is small enough that quantum effects are important.
Conservation of Energy and Momentum
2. The laws of conservation of energy and momentum provide a way to predict and describe the movement of objects. As a basis for understanding this concept:
a. Students know how to calculate kinetic energy by using the formula E= (1/2)mv2.
b. Students know how to calculate changes in gravitational potential energy near Earth by using the formula (change in potential energy) =mgh (h is the change in the elevation).
c. Students know how to solve problems involving conservation of energy in simple systems, such as falling objects.
d. Students know how to calculate momentum as the product mv.
e. Students know momentum is a separately conserved quantity different from energy.
f. Students know an unbalanced force on an object produces a change in its momentum.
g. Students know how to solve problems involving elastic and inelastic collisions in one dimension by using the principles of conservation of momentum and energy.
h.* Students know how to solve problems involving conservation of energy in simple systems with various sources of potential energy, such as capacitors and springs.
Student Objectives:
- Students will learn the application of Newtons Laws of Motions and the Laws of Energy Conversion in the working of a roller coaster. Students will work in collaboration and participate in an activity especially directed to learning the key definitions and concepts Force, Momentum, Friction, Speed, Acceleration, Gravity, Potential Energy, Kinetic Energy. Students will also learn the supporting vocabulary.
- Students will learn the accompanying mathematical formulas and units of measurement to solve problems involving kinetic energy, potential energy, force, acceleration, gravity, and mass.
- Students will design a hypothetical roller coaster and apply the concepts of Newtons laws and energy converstion covered in the lecture and guided notes to explain whether the roller coaster design will be successful or if it will fail. Students will work in collaboration and present the result of their design in class. While working on the WebQuest the student's job is to find out how roller coasters work and use this information to build a simple simulated model of a roller coaster. Students will learn about roller coaster design, laws of motion, and about velocity and acceleration. As students design their virtual roller coaster tracks students will see what happens to the roller coaster when variables such as the height of hills, the length of track, the mass of the passenger car, and speed of the coaster are changed. Finally, you will test their track with a final simulator and report the results.
- EXTENSION ACTIVITY: Students will work creatively with others to design a roller coaster in order to understand how potential energy is converted into kinetic energy. This can be done in Mesa Class or for extra credit.
Essential Unit and Content Questions:
Essential Questions: Which laws of physics apply to the design and workings of roller coasters?
Unit Questions: How is energy converted from one form to another?
Content Questions: What roles do force, velocity, potential energy, kinetic energy, weight , gravity, mass, speed and acceleration play in the workings of a roller coaster?
Unit Questions: How is energy converted from one form to another?
Content Questions: What roles do force, velocity, potential energy, kinetic energy, weight , gravity, mass, speed and acceleration play in the workings of a roller coaster?