Lecture 7 Chapter 7 Work Energy Potential Energy Kinetic Energy Energy -- The money of physics Demo: Elastic Collisions Objects of equal mass exchange momentum in elastic collisions. 1
Demo: Blaster Balls When masses unequal, momentum change can be large. Ping pong ball Speed of ping-pong ball is 3x larger (Slingshot effect) Golf ball Demo: Inelastic Collisions Objects stick together after colliding. A B A B A B 2
Check Yourself Large (4 kg) fish swims at 3 m/s towards a small (2 kg) fish (at rest) and swallows it for lunch. Total momentum before lunch? Total momentum after lunch? Velocity of the large fish (with small fish inside)? Recoil Momentum conservation also explains recoil (MASS) x (velocity) (mass) x (VELOCITY) Recoil effect is like an inelastic collision in reverse. 3
Work Define work W done on an object by a force F as (Work) = (Force) X (Distance traveled) W = F d SI Unit of Work: Joule (J) d is distance along force direction Force acting in direction of motion: Positive work. Force acting in opposite direction: Negative work. Force perpendicular to motion: Zero work Check Yourself Slaves pull a heavy load. Work done by slaves is positive, negative, or zero? Work done by friction force? Work done by the ground? Friction Support Pull LOAD 4
Work Against & By Gravity In lifting an object of weight mg by a height h, the person doing the lifting does an amount of work W = mgh. If the object is subsequently allowed to fall a distance h, gravity does work W = mgh on the object. Example: Loading Ship 3,000 kg truck is loaded onto a ship by crane that exerts upward force of 31 kn on truck. This force is applied over a distance of 2.0 m. (a) Find work done on truck by crane. (b) Find work done on truck by gravity. (c) Find net work done on the truck. Wapp = Fapp y y = (31 kn)(2.0 m) = 62 kj W mg y 2 g = y = (3000 kg)( 9.81 m/s )(2.0 m) = 58.9 kj Wnet = Wapp + Wg = (62.0 kj) + ( 58.9 kj) = 3.1 kj 5
Power (P) Power is a measure of the rate at which work is done. If work W done during time t: SI power unit: 1 J/s = 1 watt = 1 W Also: 1 horsepower = 1 hp = 746 W Human Basal Metabolism 80W 6
Example: Power of a Motor A small motor operates a lift that raises a load of bricks weighing 500 N to height of 10 m in 20 s at constant speed. Lift weighs 300 N. What is the power output of the motor? W = F d = (800N)(10m) = 8000J P = W/t = 8000J / 20s = 400 W (400 W = 0.54 hp) Energy The ability to do work. Forms of energy: Mechanical Kinetic, Potential; focus for now Thermal Chemical Electromagnetic Nuclear Energy can be transformed from one form to another Can be used in place of Newton s laws to solve certain problems more simply Energy units: SI Unit - Joule (J); Calorie (food calorie) = 4.2 kj; Kilowatt-hour = 3.6 MJ 7
Primitive Economics Do your job Get paid Modern Economics Do your job Get paid Buy stuff Using money simplifies economics and accounting. 8
Why Energy Helps Motion, in general, is hard to calculate. Using forces, momentum, acceleration, etc. gets complicated because they are all vectors (have magnitude & direction). Energy is not a vector; it s just a number. Can predict motion by figuring out how much energy that motion will cost. Potential Energy (PE) Energy an object has because of its position. Two kinds of PE in mechanics Gravitational Spring SI Unit of Potential Energy: Joule (J) PE can be positive or negative -- depends on choice of where we take PE = 0 9
Gravitational Potential Energy Gravitational potential energy of an object is (Potential Energy) = (Weight) x (Height) PE = m g h = mgh where m is mass of object in kg, h is height of object in m, and g = 9.8 N/kg = 9.8 m/s 2 Choose h = 0 to be at a convenient place Reference Level for PE PE grav A location where the gravitational potential energy is zero must be chosen for each problem The choice is arbitrary; the change in potential energy is what matters 10
Example: Bottle on Shelf A 0.350 kg bottle is on a shelf that is 1.75 m above floor. Find the gravitational potential energy of bottle-earth system when bottle is on shelf. Take potential energy = 0 when bottle on floor. PE = mgh = (0.35 kg)(9.8 N/kg)(1.75 m) = 6.0 J Sample Problem 6 kg What is the gravitational potential energy of a 6kg bowling ball at a height of 20 meters above the floor? (Take h = 0 at floor.) What is gravitational potential energy at zero height? 20 m 11
Example: Candy Bar Energy Candy bar has energy content of 212 Cal = 212 kcal = 8.87 x 10 5 J. If 81.0 kg mountain climber eats the bar, how much altitude y should she be able to gain? (Assume her body is 100% efficient engine) PE U = mgy mgy = mg y f i 5 (8.87 10 J) 2 (81.0 kg)(9.81 m/s ) PE U y = = = 1,120 m mg Kinetic Energy (KE) Energy associated with motion. Kinetic energy of an object is (Kinetic Energy) = ½ x (Mass) x (Speed) 2 KE = ½ m v 2 where m is mass of object in kg and v is speed in m/s. A stationary object has zero kinetic energy. Kinetic energy is never negative. 12
Work and Kinetic Energy An object s kinetic energy can also be thought of as the amount of work the moving object could do in coming to rest The moving hammer has kinetic energy and can do work on the nail KE Example What is the kinetic energy of a 4.0 kg hammer moving at 3.0 m/s? KE = ½mv 2 = ½(4.0 kg)(3.0 m) 2 = 18 J How much work could the hammer do on the nail? If the force needed to drive the nail is 1800N, how far would one hammer hit drive the nail? Which more effective -- double mass of hammer or double speed of hammer 13
Question Car 1 has twice the mass of Car 2, but they both have the same kinetic energy. If the speed of Car 2 is v, approximately what is the speed of Car 1? a) 0.50 v b) 0.707 v c) v d) 1.414 v e) 2.00 v Conservation of Mechanical Energy Definition of mechanical energy E: If the only work done in going from the initial to the final position is done by gravity or springs: Or equivalently: E = KE + PE When only gravity or spring forces act 14
Sample Problem 6 kg What is the kinetic energy of a 6kg bowling ball, falling from a height of 20 meters, just as it reaches the ground? 20 m 20 m/s Key Points of Lecture 7 Conservation of momentum Collisions Work Power Energy Potential Energy Kinetic Energy Mechanical Energy Before next lecture, read Hewitt through 1 st half Chap.7 Homework Assignment #4 is due before 11:00 PM on Sunday, Sept. 12. Homework Assignment #5 is due before 11:00 PM on Tuesday, Sept. 14. 15