PHYS 17200 Lecture 10: Energy Principle

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PHYS 17200 - Modern Mechanics - Lecture 10_Energy Principle
The Momentum Principle:
delta_p(system) = impulse = F_net*delta_t
delta_p(system) = effect (quantity of motion changes); vector
impulse = effect (Impulse is imparted to a System by Forces exerted by objects in
its Surroundings)
The Energy Principle:
delta_E(system) = W_surroundings + Q
delta_E(system) = change in energy of system = effect
W_surroundings = Work is done ON the System by Forces exerted by objects in
its Surroundings
Q = Energy lost as heat
ie. delta_E(system) = delta_K + delta_U => K_final + U_final = K_initial + U_initial
Similarities between the two principles
delta_p(system) + delta_p(surroundings) = 0
Newton’s 3rd Law implies that the momentum imparted to a system by
interaction with its surroundings is equal in magnitude and opposite in direction to
the momentum imparted to the surroundings by its interaction with the system.
delta_E(system) + delta_E(surroundings) = 0
We will find that the energy imparted to a system by interaction with its
surroundings is equal in magnitude and opposite in sign to the energy imparted
to the surroundings by its interaction with the system.
Energy of a Single-Particle System
Particle Energy = gamma*m*c^2
Rest Energy = m*c^2
Kinetic Energy = Particle Energy - Rest Energy = gamma*m*c^2 - m*c^2 = at high
speeds; K = ½*m*v^2 = at low speeds
gamma = 1/ sqrt(1-(v^2/c^2)) ; c = speed of light
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