Energy and Momentum

Unit 2

Overall Expectations

By the end of this course, students will:
*  demonstrate an understanding of the concepts of work, energy, momentum, and the laws of conservation of energy and of momentum for objects moving in two dimensions, and explain them in qualitative and quantitative terms;
*  investigate the laws of conservation of momentum and of energy (including elastic and inelastic collisions) through experiments or simulations, and analyse and solve problems involving these laws with the aid of vectors, graphs, and free-body diagrams;
*  analyse and describe the application of the concepts of energy and momentum to the design and development of a wide range of collision and impact-absorbing devices used in everyday life.

Specific Expectations     Understanding Basic Concepts

By the end of this course, students will:
*  define and describe the concepts and units related to momentum and energy (e.g., momentum, impulse, work-energy theorem, gravitational potential energy, elastic potential energy, thermal energy and its transfer [heat], elastic collision, inelastic collision, open and closed energy systems, simple harmonic motion);
*  analyse, with the aid of vector diagrams, the linear momentum of a collection of objects, and apply quantitatively the law of conservation of linear momentum;
*  analyse situations involving the concepts of mechanical energy, thermal energy and its transfer (heat), and the laws of conservation of momentum and of energy; distinguish between elastic and inelastic collisions;
*  analyse and explain common situations involving work and energy, using the work-energy theorem;
*  analyse the factors affecting the motion of isolated celestial objects, and calculate the gravitational potential energy for each system, as required;
*  analyse isolated planetary and satellite motion and describe it in terms of the forms of energy and energy transformations that occur (e.g., calculate the energy required to propel a spaceship from the Earth’s surface out of the Earth’s gravitational field, and describe the energy transformations that take place;
*  calculate the kinetic and gravitational potential energy of a satellite that is in a stable circular orbit around a planet);
*  state Hooke’s law and analyse it in quantitative terms.

Chapters 4, 5, & 6

Work and Energy

Potential Energy & Kinetic Energy; a series of notes
  1. My note on two topics: Momentun, Work Energy
    and Sticky Collisions
  2. Mechanics: Potential & Kinetic Energy and Conservation of Energy
    with an applet activity

    And from the Physics Classroom which may be wordy to read

    1. Potential Energy
    2. Kinetic Energy
    3. Mechanical Energy
    4. Calculating the Amount of Work Done by Forces

Hooke's Law

Hooke's law applies to the idealized case of a spring. The further you stretch the spring, the greater the force opposing the stretching, in other words, it assumes that the force increases linearly with distance. F = -kx where k is the spring constant, F is the force generated by the spring, x is the displacement from equilibrium (where F=0). Any basic sample problem will require the equation re-arranged; or substitution of another variable into the two changable variables, x and F; or balance the equation with another force (say, a mass on a spring so that F = mg).
You could also ask to determine the velocity and KE of the spring at any time or displacement of x. Or you could find the general solution to the differential equation of a harmonic oscillator, which is what you've got with a mass on a spring, and find sinusoidal motion in space, decaying exponentially with the damping constant. So it depends on what depth you need.

Hooke's Law Experiment via applet

Momentum, Impulse and Collisions

Energy and Momentum from the Physics Lab

From the Physics Classroom: Notes
  1. Momentum
  2. Momentum & Impulse Connection
  3. Momentum Conservation Principle
  4. Solving Momentum Problems
  5. Using Equations as a Guide to Thinking

  • Note on Momentum
  • From Physics 30 Note-A-Rific
    1. Linear Collisions in One Dimension
    2. Linear Collisions in Two Dimensions
    3. Elastic & Inelastic Collisons
    4. Impulse and Momentum

  • A short note on types of collisions diagrams and animation included, very helpful

    Applets which can function as labs

    1. Conservation of Momentum, Ellastic 2-D Collisions
    2. Collision Balls
    3. Conservation of Momentum
    4. 2D Collision
    5. Momentum Lab Two box cars

    6. Collisions of Red ball and Blue ball, either 1-D or 2-D, you set the angles of collision, speed, mass of balls and type of collision.

    Gravitational and Celestial Mechanics
    Kepler's Laws

    Summary of Kepler's Laws

    Kepler's laws, three mathematical statements formulated by the German astronomer Johannes Kepler that accurately describe the revolutions of the planets around the sun. Kepler's laws opened the way for the development of celestial mechanics, i.e., the application of the laws of physics to the motions of heavenly bodies. His work shows the hallmarks of great scientific theories: simplicity and universality.

    The first law states that the shape of each planet's orbit is an ellipse with the sun at one focus. The sun is thus off-center in the ellipse and the planet's distance from the sun varies as the planet moves through one orbit.
    The second law specifies quantitatively how the speed of a planet increases as its distance from the sun decreases. If an imaginary line is drawn from the sun to the planet, the line will sweep out areas in space that are shaped like pie slices. The second law states that the area swept out in equal periods of time is the same at all points in the orbit. When the planet is far from the sun and moving slowly, the pie slice will be long and narrow; when the planet is near the sun and moving fast, the pie slice will be short and fat.
    The third law establishes a relation between the average distance of the planet from the sun (the semimajor axis of the ellipse) and the time to complete one revolution around the sun (the period): the ratio of the cube of the semimajor axis to the square of the period is the same for all the planets including the earth.