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Chapter 8 Conservation of Energy 7.4 kinetic Energy and workenergy principle 8.1 Conservative forces 8.2 Potential Energy 8.3 Mechanical Energy and Its Conservationial Energy 8.4 Problem Solving Using Conservation of Mechanical Energy Question If you have a variable Force, you can find the work by finding: A) The area under a curve of Force as a function of time B) The area under a curve of Force as a function of displacement C) The slope curve of Force as a function of time D) The slope of a curve of Force as a function of displacement 7-4 Kinetic Energy and the Work-Energy Principle 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 7-4 Kinetic Energy and the Work-Energy Principle 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? (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. (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). Problem 56 56. (II) An 85-g arrow is fired from a bow whose string exerts an average force of 105 N on the arrow over a distance of 75 cm. What is the speed of the arrow as it leaves the bow? 7-4 Kinetic Energy and the Work-Energy Principle Energy was traditionally defined as the ability to do work. All forces are able to do work; however, we are dealing in these chapters with mechanical energy, which does follow this definition. 7-4 Kinetic Energy and the Work-Energy Principle If we write the acceleration in terms of the velocity and the distance, we find that the work done here is We define the kinetic energy as: 7-4 Kinetic Energy and the Work-Energy Principle This means that the work done is equal to the change in the kinetic energy: •This is the Work-Energy Principle • If the net work is positive, the kinetic energy increases. • If the net work is negative, the kinetic energy decreases. 7-4 Kinetic Energy and the Work-Energy Principle Because work and kinetic energy can be equated, they must have the same units: kinetic energy is measured in joules. Energy can be considered as the ability to do work: 8-1 Conservative and Nonconservative Forces 2 1 Example 8-1: How much work is needed to move a particle from position 1 to 2? 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. W=-mg (y2-y1) 8-1 Conservative and Nonconservative Forces Another definition of a conservative force: a force is conservative if the net work done by the force on an object moving around any closed path is zero. (a) (b) 8-1 Conservative and Nonconservative Forces If friction is present, the work done depends not only on the starting and ending points, but also on the path taken. Friction is called a non-conservative force. W = FPd 8-1 Conservative and Nonconservative Forces 8-2 Potential Energy Example 8-2 What potential energy is needed to move a block upward with an external force Fext? 8-2 Potential Energy In raising a mass m to a height h, the work done by the external force is . We therefore define the gravitational potential energy at a height y above some reference point: . 8-2 Potential Energy Example 8-3: Potential energy changes for a roller coaster. A 1000-kg roller-coaster car moves from point 1 to point 2 and then to point 3. (a) What is the gravitational potential energy at points 2 and 3 relative to point 1? That is, take y = 0 at point 1. (b) What is the change in potential energy when the car goes from point 2 to point 3? (c) Repeat parts (a) and (b), but take the reference point (y = 0) to be at point 3. Problem 7