In this unit students investigate the transfer between kinetic and potential energy on a roller coaster ride. First, students represent a roller coaster ride using a sketch of the track based on their previous experiences, video, or online simulation. Then they use the concepts of force and acceleration to describe when a rider might feel heavier or lighter than usual on the ride. This leads to a discussion of the different types of forces and resulting accelerations experienced by a rider. Students then describe the centripetal forces and accelerations required to keep the roller coaster on the track during various size curves and loops. They explore how the mass and position of an object, relative to the earth, impacts its gravitational potential energy. Last, students keep track of the transfers between kinetic and potential energies of the roller coaster during the ride. After the roller coaster reaches its highest position, it is a closed system and energy no longer enter the system. Students then use suitable initial conditions to calculate the kinetic energy and potential energy at various points on the ride and show that the total energy remains constant.
STANDARD P2: MOTION OF OBJECTS The universe is in a state of constant change. From small particles (electrons) to the large systems (galaxies) all things are in motion. Therefore, for students to understand the universe they must describe and represent various types of motion. Kinematics, the description of motion, always involves measurements of position and time. Students must describe the relationships between these quantities using mathematical statements, graphs, and motion maps. They use these representations as powerful tools to not only describe past motions but also predict future events.
P2.1 Position — Time
P2.1E Describe and classify various motions in a plane as one dimensional, two dimensional, circular, or periodic.
P2.1g Solve problems involving average speed and constant acceleration in one dimension.
P2.2A Distinguish between the variables of distance, displacement, speed, velocity, and acceleration.
P2.2B Use the change of speed and elapsed time to calculate the average acceleration for linear motion.
P2.2D State that uniform circular motion involves acceleration without a change in speed.
STANDARD P3: FORCES AND MOTION Students identify interactions between objects either as being by direct contact (e.g., pushes or pulls, friction) or at a distance (e.g., gravity, electromagnetism), and to use forces to describe interactions between objects. They recognize that non-zero net forces always cause changes in motion (Newton’s fi rst law). These changes can be changes in speed, direction, or both. Students use Newton’s second law to summarize relationships among and solve problems involving net forces, masses, and changes in motion (using standard metric units). They explain that whenever one object exerts a force on another, a force equal in magnitude and opposite in direction is exerted back on it (Newton’s third law).
P3.1 Basic Forces in Nature
P3.1A Identify the force(s) acting between objects in “direct contact” or at a distance.
P3.2A Identify the magnitude and direction of everyday forces (e.g., wind, tension in ropes, pushes and pulls, weight).
P3.4 Forces and Acceleration
P3.4B Identify forces acting on objects moving with constant velocity (e.g., cars on a highway).
P3.4C Solve problems involving force, mass, and acceleration in linear motion (Newton's second law).
P3.4D Identify the force(s) acting on objects moving with uniform circular motion (e.g., a car on a circular track, satellites in orbit).
P4.2 Energy Transformation
P4.2A Account for and represent energy transfer and transformation in complex processes (interactions).
P4.2C Explain how energy is conserved in common systems (e.g., light incident on a transparent material, light incident on a leaf, mechanical energy in a collision).
P4.3 Kinetic and Potential Energy
P4.3A Identify the form of energy in given situations (e.g., moving objects, stretched springs, rocks on cliffs, energy in food).
P4.3B Describe the transformation between potential and kinetic energy in simple mechanical systems (e.g., pendulums, roller coasters, ski lifts).
P4.3C Explain why all mechanical systems require an external energy source to maintain their motion.
P4.3x Kinetic and Potential Energy — Calculations
P4.3d Rank the amount of kinetic energy from highest to lowest of everyday examples of moving objects.
P4.3e Calculate the changes in kinetic and potential energy in simple mechanical systems (e.g., pendulums, roller coasters, ski lifts) using the formulas for kinetic energy and potential energy.
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