Subject to much change Chapter 7 Energy and Energy Transfer February 22 2006 HAPPY BIRTHDAY GEORGE Kalendar Today we start the new TOPIC OF ENERGY No Quiz on Friday but there MAY be one on Monday The BAD NEWS EXAM 2 will be on March 3 Friday ENERGY We use energy to walk run or even sleep We use energy when we lift a weight We use energy when we drive a car We even use energy to THINK BUT Introduction to Energy The concept of energy is one of the most important topics in science Every physical process that occurs in the Universe involves energy and energy transfers or transformations Energy is not easily defined Systems A system is a small portion of the Universe We identify a number of particles or objects and draw a sphere around them There are no forces acting on anything inside the sphere from outside the sphere We will ignore the details outside of the sphere A critical skill is to identify the system Valid System A valid system may be a single object or particle be a collection of objects or particles be a region of space vary in size and shape Environment There is a system boundary around the system The boundary is an imaginary surface It does not necessarily correspond to a physical boundary The boundary divides the system from the environment The environment is the rest of the Universe Work The work W done on a system by an agent exerting a constant force on the system is the product of the magnitude F of the force the magnitude r of the displacement of the point of application of the force and cos where is the angle between the force and the displacement vectors Working Working Working WORK Component of the applied force x the displacement Fcos x r Work cont W F r cos F r Later for the dot The displacement is that of the point of application of the force A force does no work on the object if the force does not move through a displacement The work done by a force on a moving object is zero when the force applied is perpendicular to the displacement of its point of application Work Example The normal force n and the gravitational force m g do no work on the object cos cos 90 0 The force F does do work on the object Same amount as in the previous overhead More About Work The system and the environment must be determined when dealing with work The environment does work on the system Work by the environment on the system The sign of the work depends on the direction of F relative to r Work is positive when projection of F onto r is in the same direction as the displacement Work is negative when the projection is in the opposite direction Units of Work Work is a scalar quantity The unit of work is a joule J 1 joule 1 newton 1 meter J N m A block of mass 2 50 kg is pushed 2 20 m along a frictionless horizontal table by a constant 16 0 N force directed 25 0 below the horizontal Determine the work done on the block by a the applied force b the normal force exerted by the table and c the gravitational force d Determine the total work done on the block A raindrop of mass 3 35 10 5 kg falls vertically at constant speed under the influence of gravity and air resistance Model the drop as a particle As it falls 100 m what is the work done on the raindrop a by the gravitational force and b by air resistance Work Is An Energy Transfer This is important for a system approach to solving a problem If the work is done on a system and it is positive energy is transferred to the system If the work done on the system is negative energy is transferred from the system Work Is An Energy Transfer cont If a system interacts with its environment this interaction can be described as a transfer of energy across the system boundary This will result in a change in the amount of energy stored in the system Shejule Continue to work on energy Exam on March 3rd Material as far as we get by March 1st Mucho WebAssign Stuf LAST TIME We defined the Dot Product We defined WORK We discussed the system and the environment System Environment Entire Universe Dumb concept WORK W F r F r cos F is the NET force acting on the block Scalar or DOT Product of Two Vectors The scalar product of two vectors is written as A B It is also called the dot product A B A B cos is the angle between A and B Scalar Product Properties The scalar product is commutative A B B A The scalar product obeys the distributive law of multiplication A B C A B A C Dot Products of Unit Vectors i i j j k k 1 i j i k j k 0 Using component form with A and B A Ax i Ay j Azk B Bx i By j Bzk A B AxBx AyBy AzBz A force F 6 i 2 j N acts on a particle that undergoes a displacement r 3 i j m Find a the work done by the force on the particle and b the angle between F and r Work Done by a Varying Force x f W Fx Dx xi xf W Fx x dx xi 11 The force acting on a particle varies as in Figure P7 11 Find the work done by the force on the particle as it moves a from x 0 to x 8 00 m b from x 8 00 m to x 10 0 m and c from x 0 to x 10 0 m Work Done By Multiple Forces AGAIN If more than one force acts on a system and the system can be modeled as a particle the total work done on the system is the work done by the net force W W net Fx dx xf xi Hooke s Law The force exerted by the spring is Fs kx x is the position of the block with respect to the equilibrium position x 0 k is called the spring constant or force constant and measures the stiffness of the spring This is called Hooke s Law Hooke s Law cont When x is positive spring is stretched F is negative When x is 0 at the equilibrium position F is 0 When x is negative spring is compressed F is positive Work Done by a Spring Identify the block as the system Calculate the work as the block moves from xi xmax to xf 0 1 2 Ws Fx dx kx dx kxmax xi xmax 2 xf 0 The total work done as the block moves from xmax to xmax is zero ENERGY IS STORED IN THE SPRING AND THEN RECOVERED AND THEN STORED AND THEN RECOVERED AND THEN STORED AND …