C6 – Introduction to Energy Get a spring General Physics

Two Minute Problems – C6T.1 Which has the larger kinetic energy, a 50-kg person running at a speed of 2 m/s or a 5-g nickel falling at a speed of 200 m/s? A. The running person B. The falling nickel C. Both have the same kinetic energy General Physics

Two Minute Problems – C6T.3 A person throws three identical rocks off a cliff of height h with exactly the same speed v0 each time (see the figure). Rock A is thrown almost vertically upward, rock B is thrown horizontally, and rock C is thrown almost vertically downward. Which rock hits the ground with the greatest speed? (Ignore friction) A. Rock A B. Rock B C. Rock C D. All rocks hit E. Other with same speed General Physics

Two Minute Problems – C6T.6 There is no way to experimentally determine the actual value of a system’s total energy, true (T) or false (F)? General Physics

Energy in interactions between two particles Total energy involved in an interaction between two particles is defined as K1 is the kinetic energy of one particle K2 is the kinetic energy of the other particle V(r) is the potential energy that depends on the distance between the particles E, K1, K2, and V(r) are all scalar quantities General Physics

Total Energy General Physics The gravitational interaction between two particles transforms gravitational potential energy to the particles’ kinetic energies without changing the system’s total energy. General Physics

Energy of multiparticle system The energy of a multiparticle system is the sum of the kinetic energies of the particles and potential energy of the interaction between the particles The potential energy of the interaction between particles 1 and 2 The kinetic energies of particles 1, 2, and 3 General Physics

Energy conserved for ISOLATED system Internal interactions between particles involves only transfers between kinetic and potential energies. The system’s total energy is not changed by these INTERNAL interactions External interactions can change the kinetic or potential energies of the particles in our system Total energy is conserved only for ISOLATED systems General Physics

Kinetic Energy Energy of a moving particle SI unit of energy General Physics

Ignore earth’s kinetic energy Ratio of kinetic energy of objects If m1 is something of normal mass, and m2 is the earth, this implies that When something of normal mass interacts with the earth, the earth’s kinetic energy can be completely ignored. General Physics

We can only measure potential energy difference We can measure the change in potential energy by comparing their positions and kinetic energies at two different times. i is the initial time and f is the next time a measurement is taken General Physics

Potential Energy Functions - C7 Electromagnetic Interaction Gravitational Interaction Potential Energy of a Spring General Physics

Gravitational potential energy One equation for the gravitational interaction potential energy z is the distance measured vertically from a reference point This equation is only valid close to the earth’s surface General Physics

Negative Energy? Only true of Potential energy Can be positive or negative with respect to a reference separation Freedom to define reference separation Kinetic energy is always positive General Physics

Conservation of Energy – Hidden Forms In future chapters, our equation for energy will include additional terms that represent energy transfers due to interactions. One example is friction, it seems to remove energy from the system. It’s actually channeling the energy into hidden forms of energy that we can’t see, such as the vibration of individual atoms Change in kinetic energy of particle 1 Change in kinetic energy of particle 2 Gravitational potential energy General Physics Hidden energy

Solving problems using framework Translation 2 pictures – initial state and final state Reference frame axes on each picture Labels for masses, velocities and separations Conceptual model diagram Interaction diagram – like momentum Include symbols inside system to show changes in kinetic and potential energies Master equation General Physics

Framework for Energy Problem – C6.2 General Physics

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Group Problems C6S.5 C7B.2 C7S.3 Each group can go at their own pace to complete the problems. General Physics