Exam II Physics 101: Lecture 9 Work and Kinetic Energy Today s lecture will be on Textbook Sections 6.1-6.4 Physics 101: Lecture 9, Pg 1
Forms Energy Kinetic Energy Motion (Today) Potential Energy Stored (Wednesday) Heat later Mass (E=mc ) phys 10 Units: Joules = kg m / s Physics 101: Lecture 9, Pg 1
Energy is Conserved Energy is Conserved meaning it can not be created nor destroyed Can change form Can be transferred Total Energy does not change with time. This is a BIG deal! Physics 101: Lecture 9, Pg 3 10
Work: Energy Transfer due to Force Force to lift trunk at constant speed Case a T a mg = 0 T = mg Case b T b - mg =0 or T = ½ mg But in case b, trunk only moves ½ distance you pull rope. F * distance is same in both! T a T b T b mg W = F dcos(q) mg Physics 101: Lecture 9, Pg 4 15
Work by Constant Force 1) ) 3) 4) Only component of force parallel to direction of motion does work! W = F d cos q q d Dr F d Dr d A) W>0 B) W=0 C) W<0 F d F F q F F W F < 0: 90< q < 180 : cos(q) < 0 W F = 0: q =90 : cos(q) =0 W F < 0: 90< q < 180 : cos(q) < 0 W F > 0: 0< q < 90 : cos(q) > 0 q F Physics 101: Lecture 9, Pg 5 18
ACTS: Ball Toss You toss a ball in the air. What is the work done by gravity as the ball goes up? A) Positive B) Negative C) Zero What is the work done by gravity as the ball goes down? A) Positive B) Negative C) Zero Physics 101: Lecture 9, Pg 6 0
Work by Constant Force Example: You pull a 30 N chest 5 meters across the floor at a constant speed by applying a force of 50 N at an angle of 30 degrees. How much work is done by the 50 N force? W = F d cos q = (50 N) (5 m) cos (30) = 17 Joules f N mg T 50 N 30 Physics 101: Lecture 9, Pg 7 1
Where did the energy go? Example: You pull a 30 N chest 5 meters across the floor at a constant speed, by applying a force of 50 N at an angle of 30 degrees. How much work did gravity do? d W = F d cos q 90 = 30 x 5 cos(90) mg = 0 How much work did friction do? N T X-Direction: SF = ma T cos(30) f = 0 f = T cos(30) W = F d cos q = 50 cos(30) x 5 cos(180) = -17 Joules f f 180 mg Physics 101: Lecture 9, Pg 8 d 5
Checkpoint Q1 You are towing a car up a hill with constant velocity. The work done on the car by the normal force is: F N T V 1. positive. negative 3. zero correct W Normal force is perpendicular to the direction of the car, so it does not contribute Physics 101: Lecture 9, Pg 9 8
Checkpoint Q You are towing a car up a hill with constant velocity. The work done on the car by the gravitational force is: F N T V 1. positive. negative 3. zero correct W The gravitational force is acting against the car going up the hill which makes it negative Physics 101: Lecture 9, Pg 10 30
Checkpoint Q3 You are towing a car up a hill with constant velocity. The work done on the car by the tension force is: 1. positive. negative 3. zero correct F N W T V The work done by the tow rope would be positive because the distance and force applied by the tow rope are both in the positive direction Physics 101: Lecture 9, Pg 11 3
Kinetic Energy: Motion Apply constant force along x-direction to a point particle m. W = F Dx = m a Dx = ½ m (v f v 0 ) = ½ m v f ½ m v 0 Work changes ½ m v recall: v f = v o + a Dx Define Kinetic Energy K = ½ m v W = D K For Point Particles Physics 101: Lecture 9, Pg 1 35
Checkpoint Q4 You are towing a car up a hill with constant velocity. The total work done on the car by all forces is: 1. positive. negative 3. zero correct F N W T V The net acceleration is 0 which means the sum of the forces is 0. Thus, work done is 0.. Physics 101: Lecture 9, Pg 13 37
Example: Block w/ friction A block is sliding on a surface with an initial speed of 5 m/s. If the coefficent of kinetic friction m k between the block and table is 0.4, how far does the block travel before stopping? Y direction: SF=ma N-mg = 0 N = mg Work W N = 0 W mg = 0 W f = f d cos(180) = -m k m g d 5 m/s f N mg W = D K -m k mg d = ½ m (v f v 0 ) -m k g d = ½ (0 v 0 ) m k g d = ½ v 0 d = ½ v 0 / m k g = 3.1 meters y x Physics 101: Lecture 9, Pg 14 44
Falling Ball Example Ball falls a distance 5 meters, What is final speed? Only force/work done by gravity W = DK W g = ½ m(v f v i ) F g d cos(0) = ½m v f mg m g d = ½m v f V f = sqrt( g d ) = 10 m/s Physics 101: Lecture 9, Pg 15 47
Work by Variable Force W = F x Dx Force Work is area under F vs x plot Spring F = k x Work Distance» Area = ½ k x =W spring Force Work Distance Physics 101: Lecture 9, Pg 16 49
Summary Energy is Conserved Work = transfer of energy using force Can be positive, negative or zero W = F d cos(q) Kinetic Energy (Motion) K = ½ m v Work = Change in Kinetic Energy S W = DK Physics 101: Lecture 9, Pg 17 50