Momentum and Energy Chapter 9, 10, 11 Physics Principles and Problems Zitzewitz, Elliot, Haase, Harper, Herzog, Nelson, Nelson, Schuler and Zorn McGraw Hill, 2005

The momentum of an object is the product of that object’s mass and velocity. p = m v Therefore a large oil tanker (big m, small v) and moving bullet (small m, big v) could have equal momentums.

An impulse changes an object’s momentum. It is the product of force on an object and the amount of time that force is applied. F ∆t = m ∆v The same impulse can be delivered in 2 ways: Increasing the force that is applied or increasing the time the force is applied. into-a-blocking-breaking-machine/karate.jpg

Impulse - Momentum Theorem F ∆t = p f - p i or F ∆t = mv f - mv i A 2200-kg car traveling at 26-m/s can be stopped in 21-s by applying the brakes or in 0.22-s by hitting a wall. What is the force exerted on the car in both of these situations? p f = 2200-kg 0-m/s = 0p i = 2200-kg 26-m/s = kg m/s F = p f - p i = -2700N OR = N ∆t

Conservation of Momentum Within any closed (no change in mass), isolated (external forces are zero) system the momentum is conserved or does not change.

m 1 v 1 + m 2 v 2 = m 1 v 3 + m 2 v 4 where v 1 and v 2 are the velocities of the objects before the collision and v 3 and v 4 new velocities after the collision. Notice the masses haven’t changed. Elastic Collisions - Objects hit and bounce off

m 1 v 1 + m 2 v 2 = (m 1 + m 2 )v 3 where v 1 and v 2 are the velocities of the objects before the collision and v 3 is the new velocities of the combined masses. Inelastic Collisions - Objects hit and stick

Energy, Work and Power Energy - the property or ability of an object to produce a change in itself or the world around it. Work - a product of the force exerted on an object in the direction of motion and the object’s displacement. W = F d (unit is the joule = Nm) Kinetic Energy - energy resulting from motion. KE = 1/2mv 2 Work-Energy Theorem - work is equal to the change in kinetic energy. W = ∆KE Work with Angle - a product of the force and the displacement, times the cosine of the angle between the force and the direction of displacement. W = Fdcos  Power - work done divided by the time taken to do the work. P = W / t (unit is the watt = J/s)

Work and Power Problems The third floor of a house is 8-m above street level. How much work is needed to move a 150-kg refrigerator to the third floor? During a tug-of-war, team A does 2.2 x J of work in pulling team B 8-m. What force did team A exert? A wagon is pulled by a force of 38-N exerted on the handle at an angle of 42° with the horizontal. If the wagon is pulled in a circle of radius 25-m, how much work is done? A lawn mower is pushed across a lawn by a force of 155-N along the direction of the handle, which is 22.5° above the horizontal. If 64.6-W of power is developed for 90-s, what distance is the mover pushed?