Ramps and Friction Teacher Guide

Unit

Ramps and Friction

Subject

Physics

Grade Level

HS

Activity Name(s)

Gravity Rules in the Skatepark

Motion on a Ramp

Being Prepared

Gravity Rules in the Skatepark

This activity would ideally be completed by individual students, with one student per computer.

The teacher may want to pace the lesson so that a set amount of time is given to the first data collection set to allow students to explore the model, but then redirect to the subsequent tasks.

Motion on a Ramp

This activity can be done in groups of 2-3 students.

If time allows, the teacher may want to have students complete the "Seeing Motion" Activity prior to this activity. This activity gives students a strong experiential understanding of position vs. time graphing.

The cardboard reflectors on the cars are necessary to get consistent data. The teacher may want to mount the cardboard onto the cars prior to the lab.

Getting Started

Gravity Rules in the Skatepark

Computers needed.

Motion on a Ramp

One set per group:

• motion sensor;
• toy car that rolls easily;
• cardboard ramp (15 cm wide and 50 cm long);
• metric ruler;
• hot melt glue gun (for teacher use only);
• book.

Suggested Timeline

The activities in this unit should take one class period each.

Thinking about the Discovery Questions

• How would skating on a half pipe be different on the moon than on the earth?

  The gravitational force between the skater and the moon would be less than the gravitational force between the skater and the earth. This would mean that there would be less acceleration due to gravity on the moon than on the earth, so the gravitational potential energy would be less. Since energy is conserved, the maximum kinetic energy would be less, so the resulting speed will be slower.

• How does gravity change the motion?

  At the maximum height, the skater will have maximum gravitational potential energy and zero kinetic energy. As the height decreases, the kinetic energy increases, so the speed will increase. When the skater reaches the bottom (zero height), the gravitational potential energy is zero, and the kinetic energy is maximum, giving the skater the maximum speed.

Misconceptions

A lighter object has more motion energy than a heavier object because lighter objects move faster than heavier objects (AAAS Project 2061, n.d.).Objects that are dropped do not have motion energy. For example, a dropped object doesn't have motion energy because gravity is just pulling it down (Herrmann-Abell & DeBoer, 2010).

Learning Objectives

• NGSS
  • Performance Expectations
    • HS-PS2-4. Use mathematical representations of Newton’s Law of Gravitation and Coulomb’s Law to describe and predict the gravitational and electrostatic forces between objects.
    • HS-PS3-1. Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known.
    • HS-PS3-2. Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative positions of particles (objects).
    • HS-PS3-4. Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).
    • HS-PS3-5. Develop and use a model of two objects interacting through electric or magnetic fields to illustrate the forces between objects and the changes in energy of the objects due to the interaction.
  • Disciplinary Core Ideas
    • HS-PS2: Motion and Stability: Forces and Interactions
      • PS2.B: Types of Interactions
        • Newton’s law of universal gravitation and Coulomb’s law provide the mathematical models to describe and predict the effects of gravitational and electrostatic forces between distant objects. (HS-PS2-4)
        • Forces at a distance are explained by fields (gravitational, electric, and magnetic) permeating space that can transfer energy through space. Magnets or electric currents cause magnetic fields; electric charges or changing magnetic fields cause electric fields. (HS-PS2-4),(HS-PS2-5)
    • HS-PS3: Energy
      • PS3.A: Definitions of Energy
        • Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as, within the system, energy is continually transferred from one object to another and between its various possible forms. (HSPS3-1),(HS-PS3-2)
        • At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy. (HS-PS3-2) (HS-PS3-3)
        • These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as either motions of particles or energy stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space. (HS-PS3-2)
      • PS3.B: Conservation of Energy and Energy Transfer
        • Conservation of energy means that the total change of energy in any system is always equal to the total energy transferred into or out of the system. (HS-PS3-1)
        • Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems. (HS-PS3-1),(HS- PS3-4)
        • Mathematical expressions, which quantify how the stored energy in a system depends on its configuration (e.g. relative positions of charged particles, compression of a spring) and how kinetic energy depends on mass and speed, allow the concept of conservation of energy to be used to predict and describe system behavior. (HS-PS3-1)
        • The availability of energy limits what can occur in any system. (HS-PS3-1)
        • Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down). (HS-PS3-4)
      • PS3.C: Relationship Between Energy and Forces
        • When two objects interacting through a field change relative position, the energy stored in the field is changed. (HS-PS3-5)
      • PS3.D: Energy in Chemical Processes and Everyday Life
        • Although energy cannot be destroyed, it can be converted to less useful forms—for example, to thermal energy in the surrounding environment. (HS-PS3-3),(HS-PS3-4)
  • Practices
    • Developing and using models
      • Develop or modify a model - based on evidence - to match what happens if a variable or component of a system is changed.
      • Develop and/or revise a model to show the relationships among variables, including those that are not observable but predict observable phenomena.
    • Using mathematics and computational thinking
      • Use mathematical representations to describe and/or support scientific conclusions and design solutions.
    • Planning and carrying out investigations
      • Conduct an investigation and/or evaluate and/or revise the experimental design to produce data to serve as the basis for evidence that meet the goals of the investigation.
  • Crosscutting Concepts
    • Patterns
      • Students recognize that macroscopic patterns are related to the nature of microscopic and atomic-level structure. They identify patterns in rates of change and other numerical relationships that provide information about natural and human designed systems. They use patterns to identify cause and effect relationships, and use graphs and charts to identify patterns in data.
    • Cause and effect
      • Students classify relationships as causal or correlational, and recognize that correlation does not necessarily imply causation. They use cause and effect relationships to predict phenomena in natural or designed systems. They also understand that phenomena may have more than one cause, and some cause and effect relationships in systems can only be described using probability.
    • Systems and system models
      • Students can understand that systems may interact with other systems; they may have sub-systems and be a part of larger complex systems. They can use models to represent systems and their interactions — such as inputs, processes and outputs — and energy, matter, and information flows within systems. They can also learn that models are limited in that they only represent certain aspects of the system under study.
    • Energy and matter: Flows, cycles, and conservation
      • Students learn matter is conserved because atoms are conserved in physical and chemical processes. They also learn within a natural or designed system, the transfer of energy drives the motion and/or cycling of matter. Energy may take different forms (e.g. energy in fields, thermal energy, energy of motion). The transfer of energy can be tracked as energy flows through a designed or natural system.
• NSES

Discussion: Setting the Stage

What is energy? Where does energy come from? Where does it go? What causes motion to change? How does gravity change motion?

The questions above can motivate a great discussion. Student answers will vary, and will reveal a great deal not only about preconceptions but also student thinking. After posing questions and discussing, consider sharing the adaptation of Richard Feynmann's Dennis the Menace building block analogy (see background.)

Discussion: Formative Questions

• What force is causing the motion?

  Gravity.

• Where is the speed of the skater minimum?

  At the bottom.

• Where is the speed of the skater maximum?

  At the top.

Discussion: Wrapping Up

• If a skater is on a planet that has half the gravity of Earth, how would his speed be different?

  1/4 speed.

• If a skater is on a planet with twice the gravity of Earth, how would his speed be different?

  sqrt 2 x

Additional Background

Gravity Rules in the Skatepark

The following analogy is from "The Feynman Lectures on Physics". Feynman, R. P., & Leighton, R. P. (1963).

Imagine Dennis has 28 blocks. They are identical to one another, absolutely indestructible, and cannot be divided into pieces.

Dennis's mother puts Dennis is in his room with his 28 blocks at the beginning of the day. At the end of each day, Dennis's mother counts the blocks and discovers a phenomenal law: No matter what he does with the blocks, there are always 28 remaining.

She replicates her experiment for some time until one day she only counts 27, but with a little searching she discovers one under a rug. She realizes she must be careful to look everywhere.

One day later she can only find 26 blocks. She looks everywhere in the room, but cannot find them. Then she realizes the window is open. She searches outside the window, and finds the two blocks outside in the garden.

Another day, she discovers 30 blocks. She gives this some thought, and realizes that Bruce has visited that day, and has left a few of his own blocks behind. Bruce's blocks are returned to him, and the experiment continues.

Like the blocks, energy cannot be created or destroyed. It may come from somewhere, and go somewhere, but the total amount remains the same.

Analysis

Gravity Rules in the Skatepark

1. What design considerations would be important for designing a skatepark on the moon? What about Jupiter?

   Student answers will vary, but may include ramp height, shape, and friction.

2. Use the language of physics to describe how skateboarding on the Moon would be different than on Earth. Would it be more exciting or less? What about Jupiter?

   The gravitational force between the skater and the moon would be less than the gravitational force between the skater and the earth. This would mean that there would be less acceleration due to gravity on the moon than on the earth, so the gravitational potential energy would be less. Since energy is conserved, the maximum kinetic energy would be less, so the resulting speed will be slower. Jupiter has more mass, so the gravitational force would be more, resulting in more gravitational potential energy. Maximum kinetic energy would be more, so the speed of the skater would be more.

3. How does gravity differ on the earth, the moon, and Jupiter? Why does it differ?

   Gravity on any planet is directly proportional to the mass of the planet, and inversely proportional to the square of the radius.

4. Describe how changes in gravity alter potential energy using the formula for potential energy.

   Gravitational potential energy is directly proportional to acceleration due to gravity, so if acceleration due to gravity increases, the gravitational potential energy will increase.

5. Describe how changes in gravity alter kinetic energy using the formula for kinetic energy.

   Kinetic energy is 1/2 mv^2, so it does not directly depend upon gravity; however, since energy is conserved within the system, if there is more gravitational potential energy, there will be more kinetic energy.

Motion on a Ramp

1. Explain the relationship between a distance vs time graph and a velocity vs time graph.

   The slope of the a line tangent to the distance vs. time graph at any point in time is the velocity.

2. How could you predict the velocity graph if you knew the shape of the distance graph?

   Examine the slope of the distance graph. What is the direction of the slope? Is it positive or negative? The slope of the a line tangent to the distance vs. time graph at any point in time is the velocity.

3. How would you predict the distance graph if you knew the shape of the velocity graph?

   The area under the velocity curve for a given time interval is the displacement for that time interval. Note: This gives the displacement from one point in time to another. In order to find a final position at the end of that time interval, the initial position must be specified.

Further Investigation

Gravity Rules in the Skatepark

The further investigation in the activity require adding in the consideration of friction. Students will see how eventually all of the energy of the system is dissipated in the form of thermal energy. This is great introduction to the second law of thermodynamics.

Motion on a Ramp

The further investigation in the activity involves investigating changing the angle of the ramp. The teacher may wish to add discussion about the effect of friction.