Physics 121 Tuesday February 26 2008 Frank L H Wolfs Department of Physics and Astronomy University of Rochester Physics 121 Tuesday February 26 2008 Course Information Quiz Topics to be discussed today Review of Conservation Laws kinetic energy potential energy conservative and con conservative forces Dissipative forces Gravitational potential energy Frank L H Wolfs Department of Physics and Astronomy University of Rochester Course information Exam 1 On Thursday February 28 between 8 am and 9 30 am the first midterm exam of Physics 121 will be held Material covered Chapters 1 6 of our text book Location Hubbell There will be a normal lecture after the exam at 9 40 am in Hoyt A Q A session on the material covered on exam 1 will take place on Tuesday evening 2 26 between 9 pm and 11 pm in Hoyt location needs to be confirmed There will be extra office hours on Tuesday 2 26 and Wednesday 2 28 Tuesday 1 4 pm B L 304 5 9 pm POA library 2 TAs Wednesday 1 3 pm B L 304 2 45 4 45 pm POA library 1 TA 7 10 pm 2 3 TAs Frank L H Wolfs Department of Physics and Astronomy University of Rochester Course information Exam 1 During workshops on Tuesday 2 26 and Wednesday 2 27 the focus will be exam 1 You can attend any or all workshops on these days Bring your questions There will be no workshops and office hours on Thursday 2 28 and Friday 2 29 You will receive the exam back during workshop during the week of March 3 Any corrections to the grades of your grade can only be made by me not by your TAs The TAs will not see the exam until you see it Frank L H Wolfs Department of Physics and Astronomy University of Rochester Physics 121 Quiz lecture 11 The quiz today will have 3 questions Frank L H Wolfs Department of Physics and Astronomy University of Rochester Conservation of energy A review The mechanical energy of a system is defined as the sum of the kinetic energy K and the potential energy U E K U If the total mechanical energy is constant we must require that E 0 or K U 0 We conclude that any change in the kinetic energy K must be accompanied by an equal but opposite change in the potential energy U Frank L H Wolfs Department of Physics and Astronomy University of Rochester Conservation of energy A review Per definition the change in potential energy is related to the work done by the force The difference between the potential energy at 2 and at 1 depends on the work done by the force F along the path between 1 and 2 The potential at 2 is only uniquely defined if the work done by the force is independent of the path Frank L H Wolfs Department of Physics and Astronomy University of Rochester Conservation of energy A review If the work is independent of the path the work around a closed path will be equal to 0 J A force for which the work is independent of the path is called a conservative force A force for which the work depends on the path is called a non conservative force Frank L H Wolfs Department of Physics and Astronomy University of Rochester Conservation of energy A review Examples of conservative forces The spring force The gravitational force Note the conservative force is sometimes directed in the direction of motion sometimes in the opposite direction Examples of non conservative forces The kinetic friction force The drag force Frank L H Wolfs Department of Physics and Astronomy University of Rochester Conservative forces Path independence The work done by any conservative force depends only on the start end end points and is independent of the path followed B d Let s proof this for gravitational force when move from A to B the we 1 mg We will consider two paths h 2 A Directly from A to B along the line connecting A and B mg mg Horizontal motion followed by vertical motion Frank L H Wolfs Department of Physics and Astronomy University of Rochester Conservative forces Path independence Path 1 direct route 1 W1 Fid mgd cos mgd sin 2 Path 2 D tour The work done by the gravitational force when you move from A in the horizontal direction is zero path and force are perpendicular The work done by the gravitational force during the vertical segment is equal to B d 1 mg Frank L H Wolfs h 2 A W1 Fid mgh cos 180 mgd sin mg mg Department of Physics and Astronomy University of Rochester Conservation of energy A review Applying conservation of mechanical energy usually simplifies our calculations However it can only be used if we care only about the relation between the initial state of a system and the final state For example conservation of mechanical energy will tell us immediately that the two kids on the two slides will have the same velocity at the bottom of the slide But we can not say anything about their relative time of arrival Frank L H Wolfs Department of Physics and Astronomy University of Rochester Conservation of energy A review Let s test our understanding of the concepts of mechanical energy and work by working on the following concept problems Q11 1 Q11 2 Q11 3 Q11 4 Note for each of these 4 problems I like to get just your opinion not a group opinion Frank L H Wolfs Department of Physics and Astronomy University of Rochester Conservation of energy Dissipative forces When dissipative forces such as friction forces are present mechanical energy is no longer conserved For example a friction force will reduce the speed of a moving object thereby dissipating its kinetic energy The amount of energy dissipated by these non conservative forces can be calculated if we know the magnitude and direction of these forces along the path followed by the object we are studying K U WNC where WNC is the work done by the non conservative forces Frank L H Wolfs Department of Physics and Astronomy University of Rochester Conservation of energy Dissipative forces When dissipative forces are present some or all of the mechanical energy is converted into internal energy The internal energy is usually in the form of heat Sharpening a pencil credit NASA Bouncing a ball credit NASA Frank L H Wolfs Department of Physics and Astronomy University of Rochester Problems with dissipative forces An example A ball bearing whose mass is m is fired vertically downward from a height h with an initial velocity v0 It buries itself in the sand at a depth d What average upward resistive force f does the sand exert on the ball as it comes to rest The initial total mechanical energy of the system is equal to m vo h y 0 f d U 0 1 Ei U i K i mgh mv0 2 2 Frank L H Wolfs Department of Physics and Astronomy University of