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

2. 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. The same impulse can be delivered in 2 ways: Increasing the force that is applied. Increasing the time the force is applied. F ∆t = m ∆v

3. Impulse - Momentum Theorem 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 = 57000 kg m/s F = p f - p i 0 - 57000 = -2700N OR 0 - 57000 = -260000N ∆t 21 0.22 F ∆t = p f - p i or F ∆t = mv f - mv i

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

5. 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 v 3 + m 2 v 4

6. 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 m 1 v 1 + m 2 v 2 = (m 1 + m 2 )v 3

7. Energy, Work and Power

8. Work and Power Problems 1.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? 1.During a tug-of-war, team A does 2.2 x 10 5 J of work in pulling team B 8 m. What force did team A exert? 1.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? 1.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?