AP Phys B Test Review Momentum and Energy 4/28/2008
Overview Momentum
• Center of Mass • Impulse-Momentum Theorem • Conservation of Momentum
Energy
• Work-Energy Theorem • Conservation of Energy • Elastic and Inelastic Collisions
Momentum
Momentum
• •
Momentum is defined as: p = m v The rate of change of momentum of an object is equal to the net force applied to the object.
∆p ΣF = ∆t
Conservation of Momentum Conservation
of momentum states that: the total momentum of an isolated system of objects remains constant.
• Isolated system: no outside forces acting on •
the system Tip: Break the momentum of each component up into horizontal and vertical components: these are independent of one another!
Collisions and Impulse
Impulse-momentum theorem defines impulse and says that the impulse on a system will be equal to the change in its momentum.
F∆t = ∆p
Center of Mass
The center-of-mass of a collection of particles if given by the following equation:
1 xCM = Σm ixi M
• •
The total linear momentum of a system of particles is equal to the total mass M of the system multiplied by the velocity of the center of mass of the system. Extended systems use this formulation for Newton’s Laws too.
Work and Energy
Work is merely a force applied on an object over a certain distance. W = F d cosθ Kinetic Energy is the energy of motion.
1 T = m v2 2
Potential Energy is the ability of an object to start/stop motion.
•
Gravity:
U = m gh
Elastic
1 2 U = kx 2
Work-Energy Theorem
This principle states that the work done on an object is equal to the change in kinetic energy of an object
W = ∆T
Conservation of Energy Conservative
vs. Non-conservative
Forces
• Friction
Conservation
of Energy: The total energy of an isolated system cannot change.
• Shift between potential and kinetic energy.
Power
Power is defined as energy over a given time period.
Collisions Elastic
Collisions
• “Rubber” – things bounce off. • Both energy and momentum are conserved.
Inelastic
Collisions
• “Gluey” – things stick together • Only momentum is conserved!
Rotational Mechanics Radians Angular
displacement, velocity, acceleration Moment of Inertia Torque Angular Momentum
Simple Harmonic Motion
Period and Frequency Oscillatory Motion
• • •
Springs, Pendulums Conservation of Energy Position as a function of time
x (t ) = A c o s (ω t )