25 Mar 2015

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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