lecture-ch9 - Contents 9 Center of Mass and Momentum 1 9.1...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Contents 9 Center of Mass and Momentum 1 9.1 The Center of Mass . . . . . . . . . . . . . . . . . . . . . . . . 1 9.1.1 Symmetry and the Center of Mass . . . . . . . . . . . 4 9.2 Newton’s Second Law for a System of Particles . . . . . . . . 7 9.3 Linear Momentum . . . . . . . . . . . . . . . . . . . . . . . . 8 9.4 The Linear Momentum of a System of Particles . . . . . . . . 8 9.5 Collision and Impulse . . . . . . . . . . . . . . . . . . . . . . . 8 9.5.1 Single Collision . . . . . . . . . . . . . . . . . . . . . . 9 9.5.2 Series of Collision . . . . . . . . . . . . . . . . . . . . . 10 9.6 Conservation of Linear Momentum . . . . . . . . . . . . . . . 11 9.7 Momentum and Kinetic Energy in Collisions . . . . . . . . . . 11 9.8 Inelastic Collisions in One Dimension . . . . . . . . . . . . . . 11 9.8.1 Completely inelastic Collision . . . . . . . . . . . . . . 12 9.8.2 Velocity of the Center of Mass . . . . . . . . . . . . . . 12 9.9 Elastic Collisions in One Dimension . . . . . . . . . . . . . . . 12 9.9.1 Stationary Target: . . . . . . . . . . . . . . . . . . . . 12 9.9.2 Moving Target: . . . . . . . . . . . . . . . . . . . . . . 13 9.10 Center of Mass Frame . . . . . . . . . . . . . . . . . . . . . . 14 9.11 Collisions in Two or Three Dimensions . . . . . . . . . . . . . 15 9.11.1 Elastic Collision in Two Dimensions . . . . . . . . . . . 16 9.12 System with Varying Mass: A Rocket . . . . . . . . . . . . . . 16 9 Center of Mass and Momentum In this chapter, we discuss how complicated motion of a system of objects can be simplified if we determine a special point of the system—the center of mass of that system. 9.1 The Center of Mass The center of mass of a system of particles in the point that moves as though (1) all of the system’s mass were concentrated there and (2) all external forces were applied here. To be more specific, for a system of N point particles of 1 mass m i at position vectorx i , the total mass of the system is M = N summationdisplay i =1 m i and the center of mass is defined as vectorx cm = 1 M N summationdisplay i =1 m i vectorx i (1) In particular, the component equations for the above are x cm = ∑ N i =1 m i x i M ,y cm = ∑ N i =1 m i y i M ,z cm = ∑ N i =1 m i z i M An ordinary object contains so many particles that we can best treat it as a continuous distribution of matter. The ”particles” then become differential mass elements dm , the sum of (1) becomes integrals vectorx cm = 1 M integraldisplay vectorxdm (2) where M = integraldisplay dm (3) The density ρ is the mass per unit volume ρ = dm dV (2) and (2) can be rewritten as M = integraldisplay dm = integraldisplay dm dV dV = integraldisplay ρdV and vectorx cm = 1 M integraldisplay ρvectorxdV If ρ is uniform, we have M = ρ integraltext dV = ρV and therefore vectorx cm = 1 V integraldisplay vectorxdV if ρ is uniform 2 For a system of N particles, we may divide it into two groups–one with N A particles, the other with the rest of N B = N − N A particles, and...
View Full Document

This note was uploaded on 05/14/2011 for the course ECON 101 taught by Professor Asdaf during the Spring '11 term at Universidad de San Buenaventura Bogota.

Page1 / 17

lecture-ch9 - Contents 9 Center of Mass and Momentum 1 9.1...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online