Chapter 6 Work, Energy, and Power
What Is Physics All About? Matter Energy Force
Work Done by a Constant Force The definition of work, when the force is parallel to the displacement: W = Fs SI unit: newton-meter (N m) = joule, J s
Work Done by a Constant Force If the force is at an angle to the displacement: W = (F cos θ)s s
Sally pulls a car with a rope. Exerting a force of 150N, she accelerates the car from rest to a speed of 5.0 km/hr in 300m. The angle of the rope is 15.0 0. The force of kinetic friction is 90.0N. What is the mass of the car? What is the work done by Sally? F y F = 150N θ = 15 F x s = 300m
Solution v i = 0m/s v f = 6.944m/s s = 300m θ = 15.0 0 F = 150N F f = 90.0N v f = v i + as 6.944 = 0 + a(300) a = 0.0804 m/s F net = ma F x F f = ma 150cos15.0 90.0 = m(0.0804) m = 683 kg W Sally = (F x + F f )s W Sally = (150cos15 + 90.0)(300) W Sally = 7.05 X 10 4 J
Work Done by a Constant Force The work done may be positive, zero, or negative, depending on the angle between the force and the displacement: s s s
Positive work accelerates an object
Negative work decelerates an object
Kinetic Energy By definition, KE = ½mv The units of KE are the same as the units of work: joules
How is Energy Related to Work? W = Fs F = ma W = mas v f = v i + as v f v i = as ½(v f v i ) = as W = m ½(v f v i ) W = ½mv f ½mv i Work-Kinetic Energy Theorem: The work done on an object is equal to its change in kinetic energy.
Power Power is a measure of the rate at which work is done: SI unit: J/s = watt 1 horsepower = 1 hp = 746 watts
Power If an object is moving at a constant speed against friction, gravity, and air resistance, the power exerted by the driving force can be written: s s
Problem Jon pulls a sled along a snowy path using a rope that makes a 45.0 angle with the ground. Jon pulls with a force of 4.3N. The sled moves at 5.33 m/s. Assuming no friction, what power does Jon produce?
Solution F = 4.3N v = 5.33s θ = 45.0 0 P = Fs t = F cosθv = (4.3)(cos45.0 )(5.33) =159w
Potential Energy Kinetic energy (KE) is the energy of motion; potential energy (PE) is stored energy. A pine cone about to fall from a certain height has PE. As it falls, the PE is released as KE. A spring that is stretched to a certain distance has PE. As it unstretches, the PE is released as KE.
Gravitational Potential Energy If we pick up a ball from one shelf and put it on a higher shelf, we have done work on the ball. There is no change in kinetic energy, but there is a change in potential energy, or PE. Like KE, it is measured in joules. PE G = mgh W = mg(h f h i ) W = mgh f mgh i h f h i = PE Gf PE Gi h f h i
Work-Energy Theorem: The total work done on an object is equal to its change in kinetic energy plus its change in potential energy plus any work done to overcome friction.
Conservation of Mechanical Energy Definition of mechanical energy: E m = KE + PE G The mechanical energy of a system is conserved. KE f + PE Gf = KE i + PE Gi Energy Skate Park
Conservation of Mechanical Energy Energy conservation can be used to solve many problems involving velocity and acceleration. Example: If I drop a 0.0 kg mass from a height of 50.0 meters, at what speed will it hit the ground? KE f + PE Gf = KE i + PE Gi KE f + 0 = 0 + PE Gi ½mv f = mgh i ½v f = gh i ½v f = (9.81)(50.0) v = 31.3 m/s
Conservation of Mechanical Energy Example: If I shoot a 10.0 g bullet straight up into the air from a height of.30 meters with a velocity of 00 m/s, how high will it go? KE f + PE Gf = KE i + PE Gi 0 + mgh f = ½mv i + mgh i (0.01)(9.81)h f = ½(0.01)(00) + (0.01)(9.81)(.30) h f =.04 km
Homework pp. 03-07 3, 31, 49, 61, 75, 93, 95 Chapter 5 Review: pp. 167-169 9, 3, 41, 6 (avg. distance from earth to sun is 149,597,890 km, v t of earth is 107,300 km/h, mass of earth is 5.98 X 10 4 kg) Chapter 4 Review: pp. 131-138 33, 41, 18