Physics 103: Lecture 8 Work and Energy

Physics 103: Lecture 8Work and Energy • Reminder: • Midterm Exam I, Thursday October 7, 5:45 - 7 PM – Locations: • Sections 302, 308, 311, 325, 327, 328 (TAs Cho & Hart ): 145 Birge • Sections 305, 306, 309, 313, 314, 315 (TAs Feintzeig & Hinojosa) : 2103 Chamberlin • Sections 303, 304, 310, 316, 322, 330 (TAs Belknap & Yip): B102 Van Vleck • Sections 307, 312, 317, 321, 329 (TAs Parker & Walker): B130 Van Vleck • Sections 301, 318, 319, 323, 324, 326 (TAs Hostetter & Hu): 1310 Sterling Physics 103, Fall 2010, UW-Madison

Exam content and exam rules • Material from Chapters 1-4 inclusive • One page of notes (8.5” x 11”) allowed • 20 multiple choice questions plus test code • Scantron will be used - bring #2 HB pencils + calculator • You must know your section number (301 - 330) & fill it in on the test • Don’t forget about practice tests !!! Physics 103, Fall 2010, UW-Madison

The 2nd Law Problems Solving • Identify force using Free Body Diagram • This is the most important step! • You may want to try drawing all the forces first and then making the free body diagram for EACH object • Set up axes and origin • x and y • perpendicular to each other • not necessarily horizontal & vertical (inclined plane) • Write Fnet=ma for each axis (components of forces) • Calculate acceleration components • Setup kinematic equations • Solve! • Suggestion: • work problem algebraically • plug in numbers only at the end Physics 103, Fall 2010, UW-Madison

Work 1D: The work that a force is doing, when that force is moving and object from point A to point B, is W =F Dx F B A Dx Work is a scalar: W > 0, when is done on the object by the external force, if there is a displacement in the same direction W < 0, if there is a displacement in the opposite direction. Units are Newton - meter, which we defined as a Joule (J). We also use calories: 1 cal = 4.186 J Physics 103, Fall 2010, UW-Madison

W =F Dx cos q Work and Force Direction Requires non-zero external force(F) and displacement (Dx) in the direction(q) of the force Physics 103, Fall 2010, UW-Madison

Work and Force Direction • No work is done on the bucket to move horizontally • Work is done in lifting the box Physics 103, Fall 2010, UW-Madison

Question 1 A woman holds up a bowling ball in a fixed position. The work she does on the ball 1. Depends on the weight of the ball. 2. Cannot be calculated without more information. 3. Is equal to zero. Although the woman is exerting force against gravity to hold the bowling ball up, she has not shifted its position. Therefore, the work done by her on the ball is zero. Physics 103, Fall 2010, UW-Madison

Question 2 A man pushes a very heavy load across a horizontal floor. The work done by gravity on the load 1. Depends on the weight of the load. 2. Depends on the coefficient of kinetic friction between the load and the floor. 3. Is equal to zero. The load is moving horizontally, whereas gravitational force is vertical. Physics 103, Fall 2010, UW-Madison

FN V T correct W Lecture 8, Preflight 1 & 2 You are towing a car up a hill with constant velocity. The work done on the car by the normal force is: 1. positive2. negative3. zero Normal force is perpendicular to displacement cosq = 0 Physics 103, Fall 2010, UW-Madison

FN V T correct W Lecture 8, Preflight 3 & 4 You are towing a car up a hill with constant velocity. The work done on the car by the gravitational force is: 1. positive2. negative3. zero There is a non-zero component of gravitational force pointing opposite the direction of motion. Physics 103, Fall 2010, UW-Madison

FN V T correct W Lecture 9, Preflight 5 & 6 You are towing a car up a hill with constant velocity. The work done on the car by the tension force is: 1. positive2. negative3. zero T is pointing in the direction of motion - therefore, work done by this force is positive. Physics 103, Fall 2010, UW-Madison

FN V T correct W Lecture 8, Preflight 7 & 8 You are towing a car up a hill with constant velocity. The total work done on the car by all forces is: 1. positive2. negative3. zero Constant velocity implies that there is no net force acting on the car, so there is no work being done overall Physics 103, Fall 2010, UW-Madison

Energy from Greek ἐνέργεια - energeia, “activity, operation” In Physics, energy is a quantity that is often understood as the ability to perform work. This quantity can be assigned to any particle, object, or system of objects as a consequence of its physical state. • Kinetic Energy • Electrical Energy • Solar Energy • Chemical Energy • Nuclear Energy • Gravitational Energy ………. Forms of energy: It is convertible into other forms ! Physics 103, Fall 2010, UW-Madison

Converting Form of Energy Physics 103, Fall 2010, UW-Madison

1 1 1 2 2 2 2 2 V = V + 2 a d 0 2 2 2 2 V - V V - V 0 0 a = W = m d 2 d 2 d 2 2 W = mV - m V 0 2 KE = mV Kinetic Energy The “energy of motion”. Work done on the object increases its energy, -- by how much? (i.e. how to calculate the value?) W = F d F = ma W = (ma) d Work-kinetic energy theorem The work done is the difference in kinetic energy

Question 3 When you do positive work on an object, its kinetic energy 1. increases. 2. decreases. 3. remains the same. 4. need more information about the way the work was done Work-energy theorem: Physics 103, Fall 2010, UW-Madison

Work Done by Gravity • Change in gravitational potential energy,DPEg = mghwork = force (mg) x distance(height) • True for any path : h, is simply the height difference, yfinal - yinitial • A falling object converts gravitational potential energy to its kinetic energy • Work needs to be done on an object to move it vertically up - work done is thesame no matter what path is taken Physics 103, Fall 2010, UW-Madison

Conservative Force • A force is conservative if work it does on an object moving between two points is independent of the path the objects take between the points • Work depends only upon initial and final positions of the object • Examples of conservative forces: • Gravity • Spring force • Electromagnetic forces Physics 103, Fall 2010, UW-Madison

correct Question 4 Suppose you want to ride your mountain bike up a steep hill. Two paths lead from the base to the top, one twice as long as the other. Compared to the average force exerted along the short path, Fav, the average force you exert along the longer path is 1. undetermined, because it depends on the time taken 2. Fav / 2 3. Fav 4. 2 Fav Gravitational potential energy gained is the same for both cases It is equal to average force exerted times distance Since distance traveled is twice, the Fav is one-half Physics 103, Fall 2010, UW-Madison

correct Question 5 Two marbles, one twice as heavy as the other, are dropped to the ground from the roof of a building. Just before hitting the ground, the heavier marble has 1. as much kinetic energy as the lighter one 2. twice as much kinetic energy as the lighter one 3. half as much kinetic energy as the lighter one 4. no kinetic energy Final velocity of the two marbles is the same Kinetic energy is proportional to mass Physics 103, Fall 2010, UW-Madison

 Summary F • Work, W = |F| |Dx| cos  • Kinetic Energy, KE = mv2/2 • Work-Kinetic Energy Theorem: • change in kinetic energy of an object = net work done on the object by all the forces ∆x • Gravitational Potential Energy: mgh

Physics 103: Lecture 8 Work and Energy