umass-physics-131-unit-3-1.1.pdf - 1 UMass Physics 131 Unit 3 Collection edited by David Nguyen Content authors David Nguyen and OpenStax Based on UMass

umass-physics-131-unit-3-1.1.pdf - 1 UMass Physics 131 Unit...

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UMass Physics 131 Unit 3 Collection edited by: David Nguyen Content authors: David Nguyen and OpenStax Based on: UMass Physics Textbook 131 < >. Online: < > This selection and arrangement of content as a collection is copyrighted by David Nguyen. Creative Commons Attribution License 4.0 Collection structure revised: 2017/08/26 PDF Generated: 2017/08/30 13:31:13 For copyright and attribution information for the modules contained in this collection, see the " Attributions " section at the end of the collection. 1
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Table of Contents Unit 3 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 Impulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Linear Momentum and Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Impulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 Conservation of Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Conservation of Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Elastic Collisions in One Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Inelastic Collisions in One Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Collisions of Point Masses in Two Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Introduction to Rocket Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3 Introduction to Torque and Center of Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Torque and Center of Mass Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Center of Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Work: The Scientific Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Representing Work Graphically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Work in Terms of Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
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UNIT 3 OVERVIEW This overview is also available as a video here () . What is the meaning of the title of this unit? Well in our last unit, we introduced the ideas of forces and Newton’s laws, and while forces are sufficient to determine the acceleration, there are clearly other quantities that are interesting if we stop and think about it. For example, it is easier to open a door by pushing on the door on the far side from the hinge where the knob is located than by pushing on the door near the hinge. If you’ve never really thought about this while opening a door, I encourage you to go try it. Similarly, if I apply a force to a ball for a short time, I get a different result than if I apply that same force for a long amount of time. If I apply the force for a long amount of time, the final velocity of the ball will be larger. For these reasons, we will be exploring in this unit forces in conjunction with other quantities. All our principles from the last unit still work, and many of these situations could be analyzed solely within the context of Newton’s laws if you need it to. However, the new ideas we’re going to introduce in this unit are often simpler to think about and to work with. However, with all the new concepts, choosing which concept to apply in each situation becomes its own unique challenge. So, let’s do a quick overview of the different concepts we’re going to talk about in this unit. The first unit we will discuss is torque, and this is the fact that where forces are applied can matter. So, this goes back to the door; applying a force near the hinge results in a different experience than applying a force far away from the hinge at the knob. The next quantity is impulse; how long
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