Work and Power W = F · x W = F x cos (ɵ)

1. Work and Power W = F ·x W = F x cos (ɵ) Work is a “dot product” or “scalar product” of two vectors, force and displacement, which yields a scalar as an answer. The sign of work is determined by the sign of the cosine of the angle between force and displacement. P = W/t Momentum Equations Momentum p = mv Impulse J = p = F t J = m v = F t Conservation of Momentum in One Dimension m1v1 + m2v2 = m1v1’ + m2v2’ Types of Collisions Elastic: momentum and kinetic energy are both conserved Inelastic: momentum is conserved Totally Inelastic: objects stick together after the collision, momentum is conserved • Conservation Laws • Read the problem. • Draw a diagram. • Write down what you know. • Write down what you want to know. • Check the units. • If you are solving an energy problem, write your conservation of energy equation with all energy terms included. • If you are solving a momentum problem, include a term for each object involved before the collision and after the collision. • Solve for the unknown. • Check to see if the answer is reasonable. Energy Equations Gravitational Potential Energy PEg = mgh Translational Kinetic Energy KEt = ½ mv2 Elastic Potential Energy PEe = ½ kx2 Rotational Kinetic Energy KEr = ½ I2 Conservation of Energy In a closed system, the total energy of a system will not change. PEg + KEt + PEe + KEr = PEg’ + KEt’ + PEe ‘+ KEr ‘ Momentum Example Energy Example Momentum Example in Two Dimensions Moment of Inertia Formulae