Physics 1408-002 Principles of Physics Sung-Won Lee [email protected] Lecture 12 – Chapter 7 & 8 – February 19, 2009 Announcement I Lecture note is on the web Handout (6 slides/page) http://highenergy.phys.ttu.edu/~slee/1408/ *** Class attendance is strongly encouraged and will be taken randomly. Also it will be used for extra credits. HW Assignment #5 will be placed on MateringPHYSICS today, and is due by 11:59pm on Wendseday, 2/25 The solutions for Exam 1 is available now; Next to my office (Sci. 117) The grades for Exam 1 is “DONE” Announcement II SI session by Reginald Tuvilla Monday 4:30 - 6:00pm - Holden Hall 106 Thursday 4:00 - 5:30pm - Holden Hall 106 SI sessions will be at the following times and location. Chapter 7 Work & Energy •!Work Done (?) by a Constant Force •!Scalar Product of Two Vectors – Math. •!Work Done by a Varying Force •!Kinetic Energy and the Work-Energy Principle 7-1 Work Done by a Constant Force The work done by a constant force is defined as the distance moved multiplied by the component of the force in the direction of displacement: where ! is the angle between the force and the displacement vectors A person pulling a crate along the floor. The work done by the force F is W = Fd cos !, where d is the displacement. 7-2 Scalar Product of Two Vectors Definition of the scalar, or dot, product: Therefore, we can write:7-3 Work Done by a Varying Force In the limit that the pieces become infinitesimally narrow, the work is the area under the curve: or: Work = Area under Fcos! curve"7-3 Work Done by a Varying Force Work done by a spring force: The force exerted by a spring is given by: x = the position of the block with respect to the equilib-rium position (x = 0) k = the spring constant and measures the stiffness of the spring •! This is called Hooke’s Law (a) Spring in normal (unstretched) position. (b) Spring is stretched by a person exerting a force FP to the right. The spring pulls back with a force FS where FS = -kx. (c) Person compresses the spring (x < 0) and the spring pushes back with a force FS = kx where FS > 0 because x < 0. 7-3 Work Done by a Varying Force Plot of F vs. x. Work done is equal to the shaded area. Work done to stretch a spring a distance x equals the triangular area under the curve F = kx. The area of a triangle is ! x base x altitude, so W = !(x)(kx) = ! kx2. –! v22 - v12 = 2a(x2-x1) = 2a"x. –! multiply by 1/2m: 1/2mv22 - 1/2mv12 = ma"x –! But F = ma 1/2mv22 - 1/2mv12 = F"x –!1/2mv22 - 1/2mv12 = F"x = WF •! We define Kinetic Energy –! K2 - K1 = Wnet –! Wnet = !K (Work/kinetic energy theorem) 7-4 Kinetic Energy and the Work-Energy Principle A change in kinetic energy is result of doing work to transfer energy into a system 7-4 Kinetic Energy and the Work-Energy Principle This means that the work done is equal to the change in the kinetic energy: •! If the net work is positive, the kinetic energy increases. •! If the net work is negative, the kinetic energy decreases. Example 7-7: Kinetic energy and work done on a baseball. A 145-g baseball is thrown so that it acquires a speed of 25 m/s. (a)!What is its kinetic energy? (b)!What was the net work done on the ball to make it reach this speed, if it started from rest?Example 7-8: Work on a car, to increase its kinetic energy. How much net work is required to accelerate a 1000-kg car from 20 m/s to 30 m/s? The net work is the increase in kinetic energy, 2.5 x 105 J. Example 7-9: Work to stop a car. A car traveling 60km/h can brake to a stop within a distance of 20 m. If the car is going twice as fast, 120 km/h, what is its stopping distance? Assume the maximum braking force is approximately independent of speed. The stopping distance increases as the square of the speed (as does the force needed to stop), so it will take 80 m. Example 7-10: A compressed spring. A horizontal spring has spring constant k = 360 N/m. (a) How much work is required to compress it from its uncompressed length (x = 0) to x = 11.0 cm? Example 7-10: A compressed spring. A horizontal spring has spring constant k = 360 N/m. (b) If a 1.85-kg block is placed against the spring and the spring is released, what will be the speed of the block when it separates from the spring at x = 0? Ignore friction Example 7-10: A compressed spring. A horizontal spring has spring constant k = 360 N/m. (c) Repeat part (b) but assume that the block is moving on a table and that some kind of constant drag force FD = 7.0 N is acting to slow it down, such as friction (or perhaps your finger). Definition of Work W = F • dr # W = F • ! r W = Fx dx # One Dimension Constant Force Definition of Kinetic Energy K = mv2 1 2 –These are Related by Newton’s Law Wtot = K2 – K1 = !K"Wtotal = Ftotal • dr # = #F • dr # Wtotal = m a • dr # – mv2 1 2 – 1 = mv2 1 2 – 2 Summary of Chapter 7 •! Work: •! Work done by a variable force: •! Kinetic energy is energy of motion: Summary of Chapter 7 •! Work-energy principle: The net work done on an object equals the change in its kinetic energy. Chapter 8 Conservation of Energy •! Conservative and Non-conservative Forces •! Potential Energy •! Mechanical Energy and Its Conservation •! Problem Solving Using Conservation of Mechanical Energy •! The Law of Conservation of Energy •! Energy Conservation with Dissipative Forces: Solving Problems •! Gravitational Potential Energy and Escape Velocity •! Power Conservation of Energy •! Energy is conserved!! (we will see this today) –! This means that energy can’t be created or destroyed –! If the total amount of energy in a system changes, it can only be due to the fact that energy has crossed the boundary of the system by energy transfer •! Mathematically, $Esystem = $T –! Esystem = Total energy of the system –! T = Energy transferred across the system boundary –! established symbols: Twork = W and Theat = Q •! The Work-Kinetic Energy theorem is a special case of Conservation of Energy"8-1 Conservative and Nonconservative Forces A force is conservative if: the work done by the force on an object moving from one point to another depends only on the initial and final positions of the object, and is independent of the particular path taken. Example: gravity. Object of mass m: (a) falls a height h vertically; (b) is raised along an arbitrary two-dimensional path.8-1 Conservative and Nonconservative Forces