7.2 Kinetic Energy and the Work-Energy Theorem

7.2 Kinetic Energy and the Work-Energy Theorem

  • The answer depends on the situation.
    • The pyramids in ancient Egypt are an example of storing energy in a system by doing work on the system.
    • The stone blocks that were lifted during the construction of the pyramids have the potential to do work.
  • The study of various types of work and forms of energy begins in this section.
    • Some types of work leave the system's energy constant, while others change the system in some way, such as making it move.
    • The energy of motion is an important form of energy.
  • Net force causes acceleration according to the study ofNewton's laws in Dynamics: Force andNewton's Laws of Motion.
  • In this section we will see that work done by the net force gives a system energy of motion, and in the process we will also find an expression for the energy of motion.
  • The total is the amount of work done on a system.
    • This is where the angle between the force and displacement are found.
  • Figure 7.3(a) shows a graph of force versus displacement for the component of the force in the direction of the displacement.
    • It is constant in this case.
    • The area under the graph is the work done.
    • The area under the curve is divided into strips with an average force.
    • The total work done is the sum of the work done for each strip.
    • The total area under the curve is a useful property that we will refer to later.
  • The force is represented by the area under the curve.
    • The total area under the curve is what the work done for each interval is.
  • Net work can be simpler if we consider a one-dimensional situation where a force is used to accelerate an object.
    • A package is pushed through the air.
  • The normal force on the package does not work because it is perpendicular to the displacement.
  • They are equal in magnitude and opposite in direction so they cancel in calculating the net force.
  • The package can be accelerated by the net force.
    • The net work done on the system is positive if the package's energy increases.
    • We can reach an interesting conclusion by usingNewton's second law and doing some math.
  • To get a relationship between net work and the speed given to a system by the net force acting on it, we take and use the equation studied in Motion Equations for Constant Acceleration in One Dimension for the change in speed over a distance if the acceleration has a constant value.
  • Solving for speed gives.
  • The net work on a system is equal to the change in the quantity.
    • The first example of a form of energy is this quantity.
  • The change in the quantity is equal to the net work on the system.
  • There is a form of energy associated with the motion of objects.
  • This means that a car traveling at 100 km/h has four times the energy of a 50 km/h car.
  • We will look at a series of examples to show different aspects of work and energy.
  • The mass and speed can be used to calculate the energy from the equation.
  • When work was first defined, the unit of work was the joule, the same as the unit of energy.
    • Although it is a large package, its energy is not large at this speed.
    • People can move packages like this without exhausting themselves.
  • The downward force from the weight of the package and the normal force have the same magnitude and opposite direction so that they cancel in calculating the net force.
    • The net work is the force times distance.
  • The push force is the net force.
  • The net work done on the package is this value.
    • The person does more work than this because of the motion.
    • Friction removes some of the energy the person uses and converts it to thermal energy.
    • The net work is the sum of the work done by each individual force.
  • The forces acting on the package are applied and gravity.
    • The normal force and force of gravity are not related to the displacement.
  • The applied force works.
  • The work done by the net force is taken into account when calculating the total work as the sum of the work by each force agrees.
    • Both approaches can be used to calculate the work done by a collection of forces.
  • The work-energy theorem can be used here because we have calculated the net work and initial energy.
    • These calculations allow us to find the final speed.
  • The final energy is the sum of the initial energy and the net work done on the package.
    • The work adds to the package's energy.